05-16-2023-1654 - Category:Phonetic transcription symbols ; count noun ; etc. (draft)

Category:Phonetic transcription symbols

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From Wikipedia, the free encyclopedia

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For more information, see phonetic transcription.

Contents

• Top
• 0–9
• A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Pages in category "Phonetic transcription symbols"

The following 109 pages are in this category, out of 109 total. This list may not reflect recent changes.

A

• Ȧ
• Ă
• Ā
• Ã
• Æ
• Latin alpha

B

• Ɓ
• Ƀ
• Small capital B
• Beta
• Bilabial click

C

• Ç
• Ć
• Ċ
• Č
• Ƈ
• Stretched C
• Ȼ
• C with bar
• Chi (letter)
• Click letter

D

• Ḍ
• African D
• Ɗ
• D with hook and tail
• D with stroke
• Eth
• Db ligature
• Double grave accent

E

• Ẽ
• Ə
• Eng (letter)
• Latin epsilon

G

• Ǧ
• Ġ
• Insular G
• Ɠ
• Glottal stop (letter)
• Gamma
• Latin gamma

ɡ

• ꬶ

H

• Ḫ
• Heng (letter)
• H with stroke
• Turned h with fishhook
• Ḥ

I

• Ɨ
• Ɪ
• Latin iota

J

• J̌

K

• K with diagonal stroke
• Ƙ
• K with stroke
• K with stroke and diagonal stroke

L

• Ł
• Barred lambda
• Latin beta
• Latin turned alpha

M

• Ɱ
• Modifier letter left half ring
• Modifier letter right half ring

N

• Ñ
• N with long right leg
• Ɲ

O

• Ɵ
• Ö
• Ǫ
• Ø
• Œ
• ⱺ
• Open O

P

• P with stroke
• Ƥ
• Palatal hook
• Phonetic Symbol Guide

Q

• Q with stroke
• Qp ligature

R

• Ȓ
• R with tail

S

• S͎
• S with swash tail
• Š
• Ṡ
• S̀
• Esh (letter)

T

• Ƭ
• Ʈ
• Theta
• Tie (typography)
• Turned A
• Turned h

U

• U bar
• Ŭ

V

• V with diagonal stroke
• Ʋ
• Turned v
• V with curl
• Voiced labiodental flap

W

• Ɯ

X

• X̣

Y

• Ý
• Ÿ (vowel)
• Yogh

Z

• Z with swash tail
• Ezh
• Ź
• Ž
• Z̀
• Ǯ

Categories:

• Letters by script
• Phonetic alphabets

Hidden categories:

• Commons category link is on Wikidata
• Template Category TOC via CatAutoTOC on category with 101–200 pages
• CatAutoTOC generates standard Category TOC

https://en.wikipedia.org/wiki/Category:Phonetic_transcription_symbols

In linguistics, a count noun (also countable noun) is a noun that can be modified by a quantity and that occurs in both singular and plural forms, and that can co-occur with quantificational determiners like every, each, several, etc. A mass noun has none of these properties: It cannot be modified by a number, cannot occur in plural, and cannot co-occur with quantificational determiners. 

https://en.wikipedia.org/wiki/Count_noun

A determiner, also called determinative (abbreviated DET), is a word, phrase, or affix that occurs together with a noun or noun phrase and generally serves to express the reference of that noun or noun phrase in the context. That is, a determiner may indicate whether the noun is referring to a definite or indefinite element of a class, to a closer or more distant element, to an element belonging to a specified person or thing, to a particular number or quantity, etc. Common kinds of determiners include definite and indefinite articles (the, a), demonstratives (this, that), possessive determiners (my, their), cardinal numerals (one, two), quantifiers (many, both), distributive determiners (each, every), and interrogative determiners (which, what). 

For the written element in logographic scripts, see Determinative.

 

https://en.wikipedia.org/wiki/Determiner

 

 

In linguistics, definiteness is a semantic feature of noun phrases, distinguishing between referents or senses that are identifiable in a given context (definite noun phrases) and those which are not (indefinite noun phrases). The prototypical definite noun phrase picks out a unique, familiar, specific referent such as the sun or Australia, as opposed to indefinite examples like an idea or some fish.

There is considerable variation in the expression of definiteness across languages, and some languages such as Japanese do not generally mark it so that the same expression could be definite in some contexts and indefinite in others. In other languages, such as English, it is usually marked by the selection of determiner (e.g., the vs a). In still other languages, such as Danish, definiteness is marked morphologically. 

https://en.wikipedia.org/wiki/Definiteness

 

 

Iron meteorites, also called siderites or ferrous meteorites, are a type of meteorite that consist overwhelmingly of an iron–nickel alloy known as meteoric iron that usually consists of two mineral phases: kamacite and taenite. Most iron meteorites originate from cores of planetesimals,^[2] with the exception of the IIE iron meteorite group^[3]

The iron found in iron meteorites was one of the earliest sources of usable iron available to humans, due to the malleability and ductility of the meteoric iron,^[4] before the development of smelting that signaled the beginning of the Iron Age. 

Iron meteorite
— Type —
Tamentit Iron Meteorite, found in 1864 in the Sahara,[1] weighing about 500 kg (1,100 lb). On display at Vulcania park in France.

https://en.wikipedia.org/wiki/Iron_meteorite

Count-classifiers and mass-classifiers

A classifier categorizes a class of nouns by picking out some salient perceptual properties...which are permanently associated with entities named by the class of nouns; a measure word does not categorize but denotes the quantity of the entity named by a noun.

— Tai (1994, p. 2), emphasis added

Within the set of nominal classifiers, linguists generally draw a distinction between "count-classifiers" and "mass-classifiers". True count-classifiers^{[note 8]} are used for naming or counting a single count noun,^[15] and have no direct translation in English; for example, 一本书 (yì běn shū, one-CL book) can only be translated in English as "one book" or "a book".^[20] Furthermore, count-classifiers cannot be used with mass nouns: just as an English speaker cannot ordinarily say *"five muds", a Chinese speaker cannot say *五个泥 (wǔ ge nì, five-CL mud). For such mass nouns, one must use mass-classifiers.^{[15][note 9]}

Mass-classifiers (true measure words) do not pick out inherent properties of an individual noun like count-classifiers do; rather, they lump nouns into countable units. Thus, mass-classifiers can generally be used with multiple types of nouns; for example, while the mass-classifier 盒 (hé, box) can be used to count boxes of lightbulbs (一盒灯泡 yì hé dēngpào, "one box of lightbulbs") or of books (一盒教材 yì hé jiàocái, "one box of textbooks"), each of these nouns must use a different count-classifier when being counted by itself (一盏灯泡 yì zhǎn dēngpào "one lightbulb"; vs. 一本教材 yì běn jiàocái "one textbook"). While count-classifiers have no direct English translation, mass-classifiers often do: phrases with count-classifiers such as 一个人 (yí ge rén, one-CL person) can only be translated as "one person" or "a person", whereas those with mass-classifiers such as 一群人 (yì qún rén, one-crowd-person) can be translated as "a crowd of people". All languages, including English, have mass-classifiers, but count-classifiers are unique to certain "classifier languages", and are not a part of English grammar apart from a few exceptional cases such as head of livestock.^[21]

Within the range of mass-classifiers, authors have proposed subdivisions based on the manner in which a mass-classifier organizes the noun into countable units. One of these is measurement units (also called "standard measures"),^[22] which all languages must have in order to measure items; this category includes units such as kilometers, liters, or pounds^[23] (see list). Like other classifiers, these can also stand without a noun; thus, for example, 磅 (bàng, pound) may appear as both 三磅肉 (sān bàng ròu, "three pounds of meat") or just 三磅 (sān bàng, "three pounds", never *三个磅 sān ge bàng).^[24] Units of currency behave similarly: for example, 十元 (shí yuán, "ten yuan"), which is short for (for example) 十元人民币 (shí yuán rénmínbì, "ten units of renminbi"). Other proposed types of mass-classifiers include "collective"^{[25][note 10]} mass-classifiers, such as 一群人 (yì qún rén, "a crowd of people"), which group things less precisely; and "container"^[26] mass-classifiers which group things by containers they come in, as in 一碗粥 (yì wǎn zhōu, "a bowl of porridge") or 一包糖 (yì bāo táng, "a bag of sugar").

The difference between count-classifiers and mass-classifiers can be described as one of quantifying versus categorizing: in other words, mass-classifiers create a unit by which to measure something (i.e. boxes, groups, chunks, pieces, etc.), whereas count-classifiers simply name an existing item.^[27] Most words can appear with both count-classifiers and mass-classifiers; for example, pizza can be described as both 一张比萨 (yì zhāng bǐsà, "one pizza", literally "one pie of pizza"), using a count-classifier, and as 一块比萨 (yí kuài bǐsà, "one piece of pizza"), using a mass-classifier. In addition to these semantic differences, there are differences in the grammatical behaviors of count-classifiers and mass-classifiers;^[28] for example, mass-classifiers may be modified by a small set of adjectives (as in 一大群人 yí dà qún rén, "a big crowd of people"), whereas count-classifiers usually may not (for example, *一大个人 yí dà ge rén is never said for "a big person"; instead the adjective must modify the noun: 一个大人 yí ge dà rén).^[29] Another difference is that count-classifiers may often be replaced by a "general" classifier 个 (個), gè with no apparent change in meaning, whereas mass-classifiers may not.^[30] Syntacticians Lisa Cheng and Rint Sybesma propose that count-classifiers and mass-classifiers have different underlying syntactic structures, with count-classifiers forming "classifier phrases",^{[note 11]} and mass-classifiers being a sort of relative clause that only looks like a classifier phrase.^[31] The distinction between count-classifiers and mass-classifiers is often unclear, however, and other linguists have suggested that count-classifiers and mass-classifiers may not be fundamentally different. They posit that "count-classifier" and "mass-classifier" are the extremes of a continuum, with most classifiers falling somewhere in between.^[32]

Verbal classifiers

There is a set of "verbal classifiers" used specifically for counting the number of times an action occurs, rather than counting a number of items; this set includes 次 cì, 遍/徧 biàn, 回 huí, and 下 xià, which all roughly translate to "times".^[33] For example, 我去过三次北京 (wǒ qù-guo sān cì Běijīng, I go-PAST three-CL Beijing, "I have been to Beijing three times").^[34] These words can also form compound classifiers with certain nouns, as in 人次 rén cì "person-time", which can be used to count (for example) visitors to a museum in a year (where visits by the same person on different occasions are counted separately).

Another type of verbal classifier indicates the tool or implement used to perform the action. An example is found in the sentence 他踢了我一脚 tā tī le wǒ yī jiǎo "he kicked me", or more literally "he kicked me one foot". The word 脚 jiǎo, which usually serves as a simple noun meaning "foot", here functions as a verbal classifier reflecting the tool (namely the foot) used to perform the kicking action.

Relation to nouns

鱼 yú
"fish"

裤子 kùzi
"(pair of) pants"

河 hé
"river"

凳子 dèngzi
"long bench"

The above nouns denoting long or flexible objects may all appear with the classifier 条 (條) tiáo in certain dialects such as Mandarin.^[35] In Mandarin, 一条板凳 means "a CL bench", and if people want to say "a chair", 個/个 or 張/张 is used because 条 is only used for referring to relatively long things. In other dialects such as Cantonese, 條 cannot be used to refer to 櫈. Instead, 張 is used.

Different classifiers often correspond to different particular nouns. For example, books generally take the classifier 本 běn, flat objects take 张 (張) zhāng, animals take 只 (隻) zhī, machines take 台 tái, large buildings and mountains take 座 zuò, etc. Within these categories are further subdivisions—while most animals take 只 (隻) zhī, domestic animals take 头 (頭) tóu, long and flexible animals take 条 (條) tiáo, and horses take 匹 pǐ. Likewise, while long things that are flexible (such as ropes) often take 条 (條) tiáo, long things that are rigid (such as sticks) take 根 gēn, unless they are also round (like pens or cigarettes), in which case in some dialects they take 枝 zhī.^[36] Classifiers also vary in how specific they are; some (such as 朵 duǒ for flowers and other similarly clustered items) are generally only used with one type, whereas others (such as 条 (條) tiáo for long and flexible things, one-dimensional things, or abstract items like news reports)^{[note 12]} are much less restricted.^[37] Furthermore, there is not a one-to-one relationship between nouns and classifiers: the same noun may be paired with different classifiers in different situations.^[38] The specific factors that govern which classifiers are paired with which nouns have been a subject of debate among linguists.

Categories and prototypes

While mass-classifiers do not necessarily bear any semantic relationship to the noun with which they are used (e.g. box and book are not related in meaning, but one can still say "a box of books"), count-classifiers do.^[31] The precise nature of that relationship, however, is not certain, since there is so much variability in how objects may be organized and categorized by classifiers. Accounts of the semantic relationship may be grouped loosely into categorical theories, which propose that count-classifiers are matched to objects solely on the basis of inherent features of those objects (such as length or size), and prototypical theories, which propose that people learn to match a count-classifier to a specific prototypical object and to other objects that are like that prototype.^[39]

The categorical, "classical"^[40] view of classifiers was that each classifier represents a category with a set of conditions; for example, the classifier 条 (條) tiáo would represent a category defined as all objects that meet the conditions of being long, thin, and one-dimensional—and nouns using that classifier must fit all the conditions with which the category is associated. Some common semantic categories into which count-classifiers have been claimed to organize nouns include the categories of shape (long, flat, or round), size (large or small), consistency (soft or hard), animacy (human, animal, or object),^[41] and function (tools, vehicles, machines, etc.).^[42]

A mule
骡子, luózi

A donkey
驴子, lǘzi

James Tai and Wang Lianqing found that the horse classifier 匹 pǐ is sometimes used for mules and camels, but rarely for the less "horse-like" donkeys, suggesting that the choice of classifiers is influenced by prototypal closeness.^[43]

On the other hand, proponents of prototype theory propose that count-classifiers may not have innate definitions, but are associated with a noun that is prototypical of that category, and nouns that have a "family resemblance" with the prototype noun will want to use the same classifier.^{[note 13]} For example, horse in Chinese uses the classifier 匹 pǐ, as in 三匹马 (sān pǐ mǎ, "three horses")—in modern Chinese the word 匹 has no meaning. Nevertheless, nouns denoting animals that look like horses will often also use this same classifier, and native speakers have been found to be more likely to use the classifier 匹 the closer an animal looks to a horse.^[43] Furthermore, words that do not meet the "criteria" of a semantic category may still use that category because of their association with a prototype. For example, the classifier 颗 (顆) kē is used for small round items, as in 一颗子弹 (yì kē zǐdàn, "one bullet"); when words like 原子弹 (yuánzǐdàn, "atomic bomb") were later introduced into the language they also used this classifier, even though they are not small and round—therefore, their classifier must have been assigned because of the words' association with the word for bullet, which acted as a "prototype".^[44] This is an example of "generalization" from prototypes: Erbaugh has proposed that when children learn count-classifiers, they go through stages, first learning a classifier-noun pair only (such as 条鱼 tiáo yú, CL-fish), then using that classifier with multiple nouns that are similar to the prototype (such as other types of fish), then finally using that set of nouns to generalize a semantic feature associated with the classifier (such as length and flexibility) so that the classifier can then be used with new words that the person encounters.^[45]

Some classifier-noun pairings are arbitrary, or at least appear to modern speakers to have no semantic motivation.^[46] For instance, the classifier 部 bù may be used for movies and novels, but also for cars^[47] and telephones.^[48] Some of this arbitrariness may be due to what linguist James Tai refers to as "fossilization", whereby a count-classifier loses its meaning through historical changes but remains paired with some nouns. For example, the classifier 匹 pǐ used for horses is meaningless today, but in Classical Chinese may have referred to a "team of two horses",^[49] a pair of horse skeletons,^[50] or the pairing between man and horse.^{[51][note 14]} Arbitrariness may also arise when a classifier is borrowed, along with its noun, from a dialect in which it has a clear meaning to one in which it does not.^[52] In both these cases, the use of the classifier is remembered more by association with certain "prototypical" nouns (such as horse) rather than by understanding of semantic categories, and thus arbitrariness has been used as an argument in favor of the prototype theory of classifiers.^[52] Gao and Malt propose that both the category and prototype theories are correct: in their conception, some classifiers constitute "well-defined categories", others make "prototype categories", and still others are relatively arbitrary.^[53]

Neutralization

In addition to the numerous "specific" count-classifiers described above,^{[note 15]} Chinese has a "general" classifier 个 (個), pronounced gè in Mandarin.^{[note 16]} This classifier is used for people, some abstract concepts, and other words that do not have special classifiers (such as 汉堡包 hànbǎobāo "hamburger"),^[54] and may also be used as a replacement for a specific classifier such as 张 (張) zhāng or 条 (條) tiáo, especially in informal speech. In Mandarin Chinese, it has been noted as early as the 1940s that the use of 个 is increasing and that there is a general tendency towards replacing specific classifiers with it.^[55] Numerous studies have reported that both adults and children tend to use 个 when they do not know the appropriate count-classifier, and even when they do but are speaking quickly or informally.^[56] The replacement of a specific classifier with the general 个 is known as classifier neutralization^[57] ("量词个化" in Chinese, literally "classifier 个-ization"^[58]). This occurs especially often among children^[59] and aphasics (individuals with damage to language-relevant areas of the brain),^[60][61] although normal speakers also neutralize frequently. It has been reported that most speakers know the appropriate classifiers for the words they are using and believe, when asked, that those classifiers are obligatory, but nevertheless use 个 without even realizing it in actual speech.^[62] As a result, in everyday spoken Mandarin the general classifier is "hundreds of times more frequent"^[63] than the specialized ones.

Nevertheless, 个 has not completely replaced other count-classifiers, and there are still many situations in which it would be inappropriate to substitute it for the required specific classifier.^[55] There may be specific patterns behind which classifier-noun pairs may be "neutralized" to use the general classifier, and which may not. Specifically, words that are most prototypical for their categories, such as paper for the category of nouns taking the "flat/square" classifier 张 (張) zhāng, may be less likely to be said with a general classifier.^[64]

Variation in usage

A painting may be referred to with the classifiers 张 (張) zhāng and 幅 fú; both phrases have the same meaning, but convey different stylistic effects.^[65]

Depending on the classifier used, the noun 楼 lóu could be used to refer to either this building, as in 一座楼 (yí zuò lóu "one building"), or the floors of the building, as in 二十层楼 (èrshí céng lóu, "twenty floors").^[66]

It is not the case that every noun is only associated with one classifier. Across dialects and speakers there is great variability in the way classifiers are used for the same words, and speakers often do not agree which classifier is best.^[67] For example, for cars some people use 部 bù, others use 台 tái, and still others use 辆 (輛) liàng; Cantonese uses 架 gaa3. Even within a single dialect or a single speaker, the same noun may take different measure words depending on the style in which the person is speaking, or on different nuances the person wants to convey (for instance, measure words can reflect the speaker's judgment of or opinion about the object^[68]). An example of this is the word for person, 人 rén, which uses the measure word 个 (個) gè normally, but uses the measure 口 kǒu when counting number of people in a household, 位 wèi when being particularly polite or honorific, and 名 míng in formal, written contexts;^[69] likewise, a group of people may be referred to by massifiers as 一群人 (yì qún rén, "a group of people") or 一帮人 (yì bāng rén, "a gang/crowd of people"): the first is neutral, whereas the second implies that the people are unruly or otherwise being judged poorly.^[70]

Some count-classifiers may also be used with nouns that they are not normally related to, for metaphorical effect, as in 一堆烦恼 (yì duī fánnǎo, "a pile of worries/troubles").^[71] Finally, a single word may have multiple count-classifiers that convey different meanings altogether—in fact, the choice of a classifier can even influence the meaning of a noun. By way of illustration, 三节课 sān jié kè means "three class periods" (as in "I have three classes today"), whereas 三门课 sān mén kè means "three courses" (as in "I signed up for three courses this semester"), even though the noun in each sentence is the same.^[66]

Purpose

In research on classifier systems, and Chinese classifiers in particular, it has been asked why count-classifiers (as opposed to mass-classifiers) exist at all. Mass-classifiers are present in all languages since they are the only way to "count" mass nouns that are not naturally divided into units (as, for example, "three splotches of mud" in English; *"three muds" is ungrammatical). On the other hand, count-classifiers are not inherently mandatory, and are absent from most languages.^{[21][note 17]} Furthermore, count-classifiers are used with an "unexpectedly low frequency";^[72] in many settings, speakers avoid specific classifiers by just using a bare noun (without a number or demonstrative) or using the general classifier 个 gè.^[73] Linguists and typologists such as Joseph Greenberg have suggested that specific count-classifiers are semantically "redundant", repeating information present within the noun.^[74] Count-classifiers can be used stylistically, though,^[69] and can also be used to clarify or limit a speaker's intended meaning when using a vague or ambiguous noun; for example, the noun 课 kè "class" can refer to courses in a semester or specific class periods during a day, depending on whether the classifier 门 (門) mén or 节 (節) jié is used.^[75]

One proposed explanation for the existence of count-classifiers is that they serve more of a cognitive purpose than a practical one: in other words, they provide a linguistic way for speakers to organize or categorize real objects.^[76] An alternative account is that they serve more of a discursive and pragmatic function (a communicative function when people interact) rather than an abstract function within the mind.^[73] Specifically, it has been proposed that count-classifiers might be used to mark new or unfamiliar objects within a discourse,^[76] to introduce major characters or items in a story or conversation,^[77] or to foreground important information and objects by making them bigger and more salient.^[78] In this way, count-classifiers might not serve an abstract grammatical or cognitive function, but may help in communication by making important information more noticeable and drawing attention to it.

History

Classifier phrases

An oracle bone inscription from the Shāng Dynasty. Such inscriptions provide some of the earliest examples of the number phrases that may have eventually spawned Chinese classifiers.

Historical linguists have found that phrases consisting of nouns and numbers went through several structural changes in Old Chinese and Middle Chinese before classifiers appeared in them. The earliest forms may have been Number – Noun, like English (i.e. "five horses"), and the less common Noun – Number ("horses five"), both of which are attested in the oracle bone scripts of Pre-Archaic Chinese (circa 1400 BCE to 1000 BCE).^[79] The first constructions resembling classifier constructions were Noun – Number – Noun constructions, which were also extant in Pre-Archaic Chinese but less common than Number – Noun. In these constructions, sometimes the first and second nouns were identical (N1 – Number – N1, as in "horses five horses") and other times the second noun was different, but semantically related (N1 – Number – N2). According to some historical linguists, the N2 in these constructions can be considered an early form of count-classifier and has even been called an "echo classifier"; this speculation is not universally agreed on, though.^[80] Although true count-classifiers had not appeared yet, mass-classifiers were common in this time, with constructions such as "wine – six – yǒu" (the word 酉 yǒu represented a wine container) meaning "six yǒu of wine".^[80] Examples such as this suggest that mass-classifiers predate count-classifiers by several centuries, although they did not appear in the same word order as they do today.^[81]

It is from this type of structure that count-classifiers may have arisen, originally replacing the second noun (in structures where there was a noun rather than a mass-classifier) to yield Noun – Number – Classifier. That is to say, constructions like "horses five horses" may have been replaced by ones like "horses five CL", possibly for stylistic reasons such as avoiding repetition.^[82] Another reason for the appearance of count-classifiers may have been to avoid confusion or ambiguity that could have arisen from counting items using only mass-classifiers—i.e. to clarify when one is referring to a single item and when one is referring to a measure of items.^[83]

Historians agree that at some point in history the order of words in this construction shifted, putting the noun at the end rather than beginning, like in the present-day construction Number – Classifier – Noun.^[84] According to historical linguist Alain Peyraube, the earliest occurrences of this construction (albeit with mass-classifiers, rather than count-classifiers) appear in the late portion of Old Chinese (500 BCE to 200 BCE). At this time, the Number – Mass-classifier portion of the Noun – Number – Mass-classifier construction was sometimes shifted in front of the noun. Peyraube speculates that this may have occurred because it was gradually reanalyzed as a modifier (like an adjective) for the head noun, as opposed to a simple repetition as it originally was. Since Chinese generally places modifiers before modified, as does English, the shift may have been prompted by this reanalysis. By the early part of the Common Era, the nouns appearing in "classifier position" were beginning to lose their meaning and become true classifiers. Estimates of when classifiers underwent the most development vary: Wang Li claims their period of major development was during the Han Dynasty (206 BCE – 220 CE),^[85] whereas Liu Shiru estimates that it was the Southern and Northern Dynasties period (420 – 589 CE),^[86] and Peyraube chooses the Tang Dynasty (618 – 907 CE).^[87] Regardless of when they developed, Wang Lianqing claims that they did not become grammatically mandatory until sometime around the 11th century.^[88]

Classifier systems in many nearby languages and language groups (such as Vietnamese and the Tai languages) are very similar to the Chinese classifier system in both grammatical structure and the parameters along which some objects are grouped together. Thus, there has been some debate over which language family first developed classifiers and which ones then borrowed them—or whether classifier systems were native to all these languages and developed more through repeated language contact throughout history.^[89]

Classifier words

Most modern count-classifiers are derived from words that originally were free-standing nouns in older varieties of Chinese, and have since been grammaticalized to become bound morphemes.^[90] In other words, count-classifiers tend to come from words that once had specific meaning but lost it (a process known as semantic bleaching).^[91] Many, however, still have related forms that work as nouns all by themselves, such as the classifier 带 (帶) dài for long, ribbon-like objects: the modern word 带子 dàizi means "ribbon".^[71] In fact, the majority of classifiers can also be used as other parts of speech, such as nouns.^[92] Mass-classifiers, on the other hand, are more transparent in meaning than count-classifiers; while the latter have some historical meaning, the former are still full-fledged nouns. For example, 杯 (bēi, cup), is both a classifier as in 一杯茶 (yì bēi chá, "a cup of tea") and the word for a cup as in 酒杯 (jiǔbēi, "wine glass").^[93]

Where do these classifiers come from? Each classifier has its own history.

— Peyraube (1991, p. 116)

It was not always the case that every noun required a count-classifier. In many historical varieties of Chinese, use of classifiers was not mandatory, and classifiers are rare in writings that have survived.^[94] Some nouns acquired classifiers earlier than others; some of the first documented uses of classifiers were for inventorying items, both in mercantile business and in storytelling.^[95] Thus, the first nouns to have count-classifiers paired with them may have been nouns that represent "culturally valued" items such as horses, scrolls, and intellectuals.^[96] The special status of such items is still apparent today: many of the classifiers that can only be paired with one or two nouns, such as 匹 pǐ for horses^{[note 18]} and 首 shǒu for songs or poems, are the classifiers for these same "valued" items. Such classifiers make up as much as one-third of the commonly used classifiers today.^[19]

Classifiers did not gain official recognition as a lexical category (part of speech) until the 20th century. The earliest modern text to discuss classifiers and their use was Ma Jianzhong's 1898 Ma's Basic Principles for Writing Clearly (马氏文通).^[97] From then until the 1940s, linguists such as Ma, Wang Li, and Li Jinxi treated classifiers as just a type of noun that "expresses a quantity".^[85] Lü Shuxiang was the first to treat them as a separate category, calling them "unit words" (单位词 dānwèicí) in his 1940s Outline of Chinese Grammar (中国文法要略) and finally "measure words" (量词 liàngcí) in Grammar Studies (语法学习). He made this separation based on the fact that classifiers were semantically bleached, and that they can be used directly with a number, whereas true nouns need to have a measure word added before they can be used with a number.^[98] After this time, other names were also proposed for classifiers: Gao Mingkai called them "noun helper words" (助名词 zhùmíngcí), Lu Wangdao "counting markers" (计标 jìbiāo), and Japanese linguist Miyawaki Kennosuke called them "accompanying words" (陪伴词 péibàncí).^[99] In the Draft Plan for a System of Teaching Chinese Grammar [zh] adopted by the People's Republic of China in 1954, Lü's "measure words" (量词 liàngcí) was adopted as the official name for classifiers in China.^[100] This remains the most common term in use today.^[12]

General classifiers

Historically, 个 gè was not always the general classifier. Some believe it was originally a noun referring to bamboo stalks, and gradually expanded in use to become a classifier for many things with "vertical, individual, [or] upright qualit[ies]",^[101] eventually becoming a general classifier because it was used so frequently with common nouns.^[102] The classifier gè is actually associated with three different homophonous characters: 个, 個 (used today as the traditional-character equivalent of 个), and 箇. Historical linguist Lianqing Wang has argued that these characters actually originated from different words, and that only 箇 had the original meaning of "bamboo stalk".^[103] 个, he claims, was used as a general classifier early on, and may have been derived from the orthographically similar 介 jiè, one of the earliest general classifiers.^[104] 箇 later merged with 介 because they were similar in pronunciation and meaning (both used as general classifiers).^[103] Likewise, he claims that 個 was also a separate word (with a meaning having to do with "partiality" or "being a single part"), and merged with 个 for the same reasons as 箇 did; he also argues that 個 was "created", as early as the Han Dynasty, to supersede 个.^[105]

Nor was 个 the only general classifier in the history of Chinese. The aforementioned 介 jiè was being used as a general classifier before the Qin Dynasty (221 BCE); it was originally a noun referring to individual items out of a string of connected shells or clothes, and eventually came to be used as a classifier for "individual" objects (as opposed to pairs or groups of objects) before becoming a general classifier.^[106] Another general classifier was 枚 méi, which originally referred to small twigs. Since twigs were used for counting items, 枚 became a counter word: any items, including people, could be counted as "one 枚, two 枚", etc. 枚 was the most common classifier in use during the Southern and Northern Dynasties period (420–589 CE),^[107] but today is no longer a general classifier, and is only used rarely, as a specialized classifier for items such as pins and badges.^[108] Kathleen Ahrens has claimed that 隻 (zhī in Mandarin and jia in Taiwanese), the classifier for animals in Mandarin, is another general classifier in Taiwanese and may be becoming one in the Mandarin spoken in Taiwan.^[109]

Variety

Northern dialects tend to have fewer classifiers than southern ones. 個 ge is the only classifier found in the Dungan language. All nouns could have just one classifier in some dialects, such as Shanghainese (Wu), the Mandarin dialect of Shanxi, and Shandong dialects. Some dialects such as Northern Min, certain Xiang dialects, Hakka dialects, and some Yue dialects use 隻 for the noun referring to people, rather than 個.^[110]

See also

• China portal
• Languages portal

• List of Chinese classifiers
• Chinese grammar
• Collective noun
• Classifiers in other languages:
  • Burmese numerical classifiers
  • Hokkien counter word
  • Japanese counter word
  • Korean counter word
  • Vietnamese classifier

Notes

1. 
   

All examples given in this article are from standard Mandarin Chinese, with pronunciation indicated using the pinyin system, unless otherwise stated. The script would often be identical in other varieties of Chinese, although the pronunciation would vary.

Across different varieties of Chinese, classifier-noun clauses have slightly different interpretations (particularly in the interpretation of definiteness in classified nouns as opposed to bare nouns), but the requirement that a classifier come between a number and a noun is more or less the same in the major varieties (Cheng & Sybesma 2005).

Although “每” (每个人) is more generally used to mean "every person" in this case.

See, for example, similar results in the Chinese corpus of the Center for Chinese Linguistics at Peking University: 天空一片, retrieved on 3 June 2009.

In addition to the count-mass distinction and nominal-verbal distinction described below, various linguists have proposed many additional divisions of classifiers by type. He (2001, chapters 2 and 3) contains a review of these.

The Syllabus of Graded Words and Characters for Chinese Proficiency is a standardized measure of vocabulary and character recognition, used in the People's Republic of China for testing middle school students, high school students, and foreign learners. The most recent edition was published in 2003 by the Testing Center of the National Chinese Proficiency Testing Committee.

Including the following:

• Chen, Baocun 陈保存 (1988). Chinese Classifier Dictionary 汉语量词词典. Fuzhou: Fujian People's Publishing House 福建人民出版社. ISBN 978-7-211-00375-4.
• Fang, Jiqing; Connelly; Michael (2008). Chinese Measure Word Dictionary. Boston: Cheng & Tsui. ISBN 978-0-88727-632-3.
• Jiao, Fan 焦凡 (2001). A Chinese-English Dictionary of Measure Words 汉英量词词典. Beijing: Sinolingua 华语敎学出版社. ISBN 978-7-80052-568-1.
• Liu, Ziping 刘子平 (1996). Chinese Classifier Dictionary 汉语量词词典. Inner Mongolia Education Press 内蒙古教育出版社. ISBN 978-7-5311-2707-9.

Count-classifiers have also been called "individual classifiers", (Chao 1968, p. 509), "qualifying classifiers" (Zhang 2007, p. 45; Hu 1993, p. 10), and just "classifiers" (Cheng & Sybesma 1998, p. 3).

Mass-classifiers have also been called "measure words", "massifiers" (Cheng & Sybesma 1998, p. 3), "non-individual classifiers" (Chao 1968, p. 509), and "quantifying classifiers" (Zhang 2007, p. 45; Hu 1993, p. 10). The term "mass-classifier" is used in this article to avoid ambiguous usage of the term "measure word", which is often used in everyday speech to refer to both count-classifiers and mass-classifiers, even though in technical usage it only means mass-classifiers (Li 2000, p. 1116).

Also called "aggregate" (Li & Thompson 1981, pp. 107–109) or "group" (Ahrens 1994, p. 239, note 3) measures.

"Classifier phrases" are similar to noun phrases, but with a classifier rather than a noun as the head (Cheng & Sybesma 1998, pp. 16–17).

This may be because official documents during the Han Dynasty were written on long bamboo strips, making them "strips of business" (Ahrens 1994, p. 206).

The theory described in Ahrens (1994) and Wang (1994) is also referred to within those works as a "prototype" theory, but differs somewhat from the version of prototype theory described here; rather than claiming that individual prototypes are the source for classifier meanings, these authors believe that classifiers still are based on categories with features, but that the categories have many features, and "prototypes" are words that have all the features of that category whereas other words in the category only have some features. In other words, "there are core and marginal members of a category.... a member of a category does not necessarily possess all the properties of that category" (Wang 1994, p. 8). For instance, the classifier 棵 kē is used for the category of trees, which may have features such as "has a trunk", "has leaves", and "has branches", "is deciduous"; maple trees would be prototypes of the category, since they have all these features, whereas palm trees only have a trunk and leaves and thus are not prototypical (Ahrens 1994, pp. 211–12).

The apparent disagreement between the definitions provided by different authors may reflect different uses of these words in different time periods. It is well-attested that many classifiers underwent frequent changes of meaning throughout history (Wang 1994; Erbaugh 1986, pp. 426–31; Ahrens 1994, pp. 205–206), so 匹 pǐ may have had all these meanings at different points in history.

Also called "sortal classifiers" (Erbaugh 2000, p. 33; Biq 2002, p. 531).

Kathleen Ahrens claimed in 1994 that the classifier for animals—只 (隻), pronounced zhī in Mandarin and jia in Taiwanese—is in the process of becoming a second general classifier in the Mandarin spoken in Taiwan, and already is used as the general classifier in Taiwanese itself (Ahrens 1994, p. 206).

Although English does not have a productive system of count-classifiers and is not considered a "classifier language", it does have a few constructions—mostly archaic or specialized—that resemble count-classifiers, such as "X head of cattle" (T'sou 1976, p. 1221).

18. Today, 匹 may also be used for bolts of cloth. See "List of Common Nominal Measure Words" on ChineseNotes.com (last modified 11 January 2009; retrieved on 3 September 2009).

References

1. 
   

Li & Thompson 1981, p. 104

Hu 1993, p. 13

The examples are adapted from those given in Hu (1993, p. 13), Erbaugh (1986, pp. 403–404), and Li & Thompson (1981, pp. 104–105).

Zhang 2007, p. 47

Li 2000, p. 1119

Sun 2006, p. 159

Sun 2006, p. 160

Li & Thompson 1981, p. 82

Li & Thompson 1981, pp. 34–35

Li & Thompson 1981, p. 111

Hu 1993, p. 9

Li 2000, p. 1116; Hu 1993, p. 7; Wang 1994, pp. 22, 24–25; He 2001, p. 8. Also see the usage in Fang & Connelly (2008) and most introductory Chinese textbooks.

Li & Thompson 1981, p. 105

Chao 1968, section 7.9

Zhang 2007, p. 44

Erbaugh 1986, p. 403; Fang & Connelly 2008, p. ix

He 2001, p. 234

Gao & Malt 2009, p. 1133

Erbaugh 1986, p. 403

Erbaugh 1986, p. 404

Tai 1994, p. 3; Allan 1977, pp. 285–86; Wang 1994, p. 1

Ahrens 1994, p. 239, note 3

Li & Thompson 1981, p. 105; Zhang 2007, p. 44; Erbaugh 1986, p. 118, note 5

Li & Thompson 1981, pp. 105–107

Erbaugh 1986, p. 118, note 5; Hu 1993, p. 9

Erbaugh 1986, p. 118, note 5; Li & Thompson 1981, pp. 107–109

Cheng & Sybesma 1998, p. 3; Tai 1994, p. 2

Wang 1994, pp. 27–36; Cheng & Sybesma 1998

Cheng & Sybesma 1998, pp. 3–5

Wang 1994, pp. 29–30

Cheng & Sybesma 1998

Ahrens 1994, p. 239, note 5; Wang 1994, pp. 26–27, 37–48

He 2001, pp. 42, 44

Zhang 2007, p. 44; Li & Thompson 1981, p. 110; Fang & Connelly 2008, p. x

Tai 1994, p. 8

Tai 1994, pp. 7–9; Tai & Wang 1990

Erbaugh 1986, p. 111

He 2001, p. 239

Tai 1994, pp. 3–5; Ahrens 1994, pp. 208–12

Tai 1994, p. 3; Ahrens 1994, pp. 209–10

Tai 1994, p. 5; Allan 1977

Hu 1993, p. 1

Tai 1994, p. 12

Zhang 2007, pp. 46–47

Erbaugh 1986, p. 415

Hu 1993, p. 1; Tai 1994, p. 13; Zhang 2007, pp. 55–56

Zhang 2007, pp. 55–56

Gao & Malt 2009, p. 1134

Morev 2000, p. 79

Wang 1994, pp. 172–73

Tai 1994, p. 15, note 7

Tai 1994, p. 13

Gao & Malt 2009, pp. 1133–4

Hu 1993, p. 12

Tzeng, Chen & Hung 1991, p. 193

Zhang 2007, p. 57

Ahrens 1994, p. 212

He 2001, p. 165

Erbaugh 1986; Hu 1993

Ahrens 1994, pp. 227–32

Tzeng, Chen & Hung 1991

Erbaugh 1986, pp. 404–406; Ahrens 1994, pp. 202–203

Erbaugh 1986, pp. 404–406

Ahrens 1994

Zhang 2007, p. 53

Zhang 2007, p. 52

Tai 1994; Erbaugh 2000, pp. 34–35

He 2001, p. 237

Fang & Connelly 2008, p. ix; Zhang 2007, pp. 53–54

He 2001, p. 242

Shie 2003, p. 76

Erbaugh 2000, p. 34

Erbaugh 2000, pp. 425–26; Li 2000

Zhang 2007, p. 51

Zhang 2007, pp. 51–52

Erbaugh 1986, pp. 425–6

Sun 1988, p. 298

Li 2000

Peyraube 1991, p. 107; Morev 2000, pp. 78–79

Peyraube 1991, p. 108

Peyraube 1991, p. 110; Wang 1994, pp. 171–72

Morev 2000, pp. 78–79

Wang 1994, p. 172

Peyraube 1991, p. 106; Morev 2000, pp. 78–79

He 2001, p. 3

Wang 1994, pp. 2, 17

Peyraube 1991, pp. 111–17

Wang 1994, p. 3

Erbaugh 1986, p. 401; Wang 1994, p. 2

Shie 2003, p. 76; Wang 1994, pp. 113–14, 172–73

Peyraube 1991, p. 116

Gao & Malt 2009, p. 1130

Chien, Lust & Chiang 2003, p. 92

Peyraube 1991; Erbaugh 1986, p. 401

Erbaugh 1986, p. 401

Erbaugh 1986, pp. 401, 403, 428

He 2001, p. 2

He 2001, p. 4

He 2001, pp. 5–6

He 2001, p. 7

Erbaugh 1986, p. 430

Erbaugh 1986, pp. 428–30; Ahrens 1994, p. 205

Wang 1994, pp. 114–15

Wang 1994, p. 95

Wang 1994, pp. 115–16, 158

Wang 1994, pp. 93–95

Wang 1994, pp. 155–7

Erbaugh 1986, p. 428

Ahrens 1994, p. 206

110. Graham Thurgood; Randy J. LaPolla (2003). Graham Thurgood, Randy J. LaPolla (ed.). The Sino-Tibetan languages. Routledge language family. Vol. 3 (illustrated ed.). Psychology Press. p. 85. ISBN 0-7007-1129-5. Retrieved 2012-03-10. In general, the Southern dialects have a greater number of classifiers than the Northern. The farther north one travels, the smaller the variety of classifiers found. In Dunganese, a Gansu dialect of Northern Chinese spoken in Central Asia, only one classifier, 個 [kə], is used; and this same classifier has almost become the cover classifier for all nouns in Lánzhou of Gansu too. The tendency to use one general classifier for all nouns is also found to a greater or lesser extent in many Shanxi dialects, some Shandong dialects, and even the Shanghai dialect of Wu and Standard Mandarin (SM). The choice of classifiers for individual nouns is particular to each dialect. For example, although the preferred classifier across dialects for 'human being' is 個 and its cognates, 隻 in its dialect forms is widely used in the Hakka and Yue dialects of Guangxi and western Guangdong provinces as well as in the Northern Min dialects and some Xiang dialects in Hunan.

Bibliography

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• Allan, Keith (1977). "Classifiers". Language. Linguistic Society of America. 53 (2): 285–311. doi:10.2307/413103. JSTOR 413103.
• Biq, Yung-O (2002). "Classifier and construction: the interaction of grammatical categories and cognitive strategies" (PDF). Language and Linguistics. 3 (3): 521–42. Archived from the original (PDF) on 2019-07-11.
• Chao, Yuen Ren (1968). A Grammar of Spoken Chinese. Berkeley: University of California Press.
• Cheng, Lisa L.-S.; Sybesma, Rint (1998). "yi-wan tang and yi-ge Tang: Classifiers and mass-classifiers". Tsing Hua Journal of Chinese Studies. 28 (3).
• Cheng, Lisa L.-S.; Sybesma, Rint (2005). "Classifiers in four varieties of Chinese". In Cinque, Guglielmo; Kayne, Richard S. (eds.). The Oxford Handbook of Comparative Syntax. Oxford University Press. ISBN 0-19-513650-0.
• Chien, Yu-Chin; Lust, Barbara; Chiang, Chi-Pang (2003). "Chinese children's comprehension of count-classifiers and mass-classifiers". Journal of East Asian Linguistics. 12 (2): 91–120. doi:10.1023/A:1022401006521.
• Erbaugh, Mary S. (1986). "Taking stock: the development of Chinese noun classifiers historically and in young children". In Colette Craig (ed.). Noun classes and categorization. J. Benjamins. pp. 399–436. ISBN 978-0-915027-33-0.
• Erbaugh, Mary S. (2000). Classifiers are for specification: complementary functions for sortal and general classifiers in Cantonese and Mandarin. 33rd International Conference on Sino-Tibetan Languages and Linguistics.
• Fang, Jiqing; Connelly, Michael (2008). Chinese Measure Word Dictionary. Boston: Cheng & Tsui. ISBN 978-0-88727-632-3.
• Gao, Ming; Malt, Barbara (2009). "Mental representation and cognitive consequences of Chinese individual classifiers". Language and Cognitive Processes. 24 (7/8): 1124–1179. doi:10.1080/01690960802018323.
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External links

• List of Common Nominal Measure Words on chinesenotes.com
• Units of Weights and Measures on chinesenotes.com
• How to Use Chinese Measure Words on 3000 Hanzi

v t e Chinese language or Sinitic languages

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Single-crystalline GeTe nanowires and nanohelices

Semiconducting GeTe nanowires (NW) and nanohelices (NH) are synthesized via vapor transport method, with metal nanoparticle catalysts. GeTe was evaporated and carried by Ar gas at optimum temperature, pressure, time, and gas flow rate to the downstream collecting/grow site (SiO₂ surface coated with colloidal gold nanoparticles). High temperature over 500 °C produces thicker nanowires and crystalline chunks. Au is essential to the growth of NW and NH and is suggested to the metal catalyst of the reaction. This method gives rise to NW and NH with a 1:1 ratio of Ge and Te. NW produced by this method average about 65 nm in diameter and up to 50 μm in length. NHs averages to 135 nm in helix diameter.^[9]

Nanocrystal (quantum size effect)

The synthesis described above has not reached the sized required to exhibit quantum size effect. Nanostructures that reach the quantum regime exhibit a different set of phenomena unseen at a larger scale, for example, spontaneous polar ordering and the splitting of diffraction spots. The synthesis of GeTe nanocrystals of average size of 8, 17, and 100 nm involves divalent Ge(II) chloride – 1,4 dioxane complex and bis[bis(trimethylsilyl)amino]Ge (II) and trioctylphosphine-tellurium in a solvent such as 1,2-dichlorobenzene or phenyl ether. Ge(II) reduction kinetics has been thought to determine the GeTe formation. Large the Ge(II) reduction rate may lead to the increase in particle nucleation rate, resulting in the reduction of particle diameter.^[10] 

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"Hymn to the Fallen" (Jiu Ge) (traditional Chinese: 國殤; simplified Chinese: 国殇; pinyin: Guó shāng; lit. 'National casualties') is a Classical Chinese poem which has been preserved in the Nine Songs (Jiu Ge) section of the ancient Chinese poetry anthology, the Chu ci, or The Songs of Chu, which is an ancient set of poems. Together, these poems constitute one of the 17 sections of the poetry anthology which was published under the title of the Chuci (also known as the Songs of Chu or as the Songs of the South). Despite the "Nine" in the title (Jiu ge literally means Nine Songs), the number of these poetic pieces actually consists of eleven separate songs, or elegies.^[1] This set of verses seems to represent some shamanistic dramatic practices of the Yangzi River valley area (as well as a northern tradition or traditions) involving the invocation of divine beings and seeking their blessings by means of a process of courtship.^[2] The poetry consists of lyrics written for performance as part of a religious drama, however the lack of stage directions or indications of who is supposed to be singing at any one time or whether some of the lines represent lines for a chorus makes an accurate reconstruction of how such a shamanic drama would actually have been performed quite uncertain; although, there are internal textual clues, for example indicating the use of spectacular costumes for the performers, and an extensive orchestra.^[3] Although not precisely dated, "Hymn to the Fallen" dates from the end of the late the Warring States period, ended 221 BCE, with possible revisions in the Han dynasty, particularly during the reign of Han Wudi, during 141 to 87 BCE . The poem has been translated into English by David Hawkes as "Hymn to the Fallen". "Guo shang" is a hymn to soldiers killed in war. Guó (國) means the "state", "kingdom", or "nation". Shāng (殤) means to "die young". Put together, the title refers to those who meet death in the course of fighting for their country. David Hawkes describes it as "surely one of the most beautiful laments for fallen soldiers in any language".^[4] 

https://en.wikipedia.org/wiki/Hymn_to_the_Fallen_(Jiu_Ge)

 

 

https://en.wikipedia.org/wiki/Neologism https://en.wikipedia.org/wiki/Origin_of_language https://en.wikipedia.org/wiki/Language_acquisition https://en.wikipedia.org/wiki/Computer_language https://en.wikipedia.org/wiki/ISO_(disambiguation) https://en.wikipedia.org/wiki/Phonemic_awareness https://en.wikipedia.org/wiki/Recognition_memory https://en.wikipedia.org/wiki/Processor https://en.wikipedia.org/wiki/Processor_register https://en.wikipedia.org/wiki/Procession https://en.wikipedia.org/wiki/Computer_architecture https://en.wikipedia.org/wiki/Memory_address https://en.wikipedia.org/wiki/Computer_data_storage#Primary_storage https://en.wikipedia.org/wiki/Static_random-access_memory https://en.wikipedia.org/wiki/Load%E2%80%93store_architecture https://en.wikipedia.org/wiki/Potential_energy https://en.wikipedia.org/wiki/Accumulator https://en.wikipedia.org/wiki/Instruction_set_architecture https://en.wikipedia.org/wiki/Speculative_execution https://en.wikipedia.org/wiki/Program_optimization A processor register is a quickly accessible location available to a computer's processor.[1] Registers usually consist of a small amount of fast storage, although some registers have specific hardware functions, and may be read-only or write-only. In computer architecture, registers are typically addressed by mechanisms other than main memory, but may in some cases be assigned a memory address e.g. DEC PDP-10, ICT 1900.[2] Almost all computers, whether load/store architecture or not, load items of data from a larger memory into registers where they are used for arithmetic operations, bitwise operations, and other operations, and are manipulated or tested by machine instructions. Manipulated items are then often stored back to main memory, either by the same instruction or by a subsequent one. Modern processors use either static or dynamic RAM as main memory, with the latter usually accessed via one or more cache levels. Processor registers are normally at the top of the memory hierarchy, and provide the fastest way to access data. The term normally refers only to the group of registers that are directly encoded as part of an instruction, as defined by the instruction set. However, modern high-performance CPUs often have duplicates of these "architectural registers" in order to improve performance via register renaming, allowing parallel and speculative execution. Modern x86 design acquired these techniques around 1995 with the releases of Pentium Pro, Cyrix 6x86, Nx586, and AMD K5. When a computer program accesses the same data repeatedly, this is called locality of reference. Holding frequently used values in registers can be critical to a program's performance. Register allocation is performed either by a compiler in the code generation phase, or manually by an assembly language programmer. https://en.wikipedia.org/wiki/Processor_register Size Registers are normally measured by the number of bits they can hold, for example, an "8-bit register", "32-bit register", "64-bit register", or even more. In some instruction sets, the registers can operate in various modes, breaking down their storage memory into smaller parts (32-bit into four 8-bit ones, for instance) to which multiple data (vector, or one-dimensional array of data) can be loaded and operated upon at the same time. Typically it is implemented by adding extra registers that map their memory into a larger register. Processors that have the ability to execute single instructions on multiple data are called vector processors. https://en.wikipedia.org/wiki/Processor_register A geolocation-based video game or location-based video game is a type of video game where the gameplay evolves and progresses via a player's location in the world, often attained using GPS. Most location-based video games are mobile games that make use of the mobile phone's built in GPS capability, and often have real-world map integration. One of the most recognizable location-based mobile games is Pokémon Go. Location-based (GPS) games are often conflated with augmented reality (AR) games. GPS and AR are two separate technologies which are sometimes both used in a game, like in Pokémon Go and Minecraft Earth. GPS and AR functionality largely do not depend on one another but are often used in concert. A video game may be an AR game, a location-based game, both, or neither. https://en.wikipedia.org/wiki/Geolocation-based_video_game https://en.wikipedia.org/wiki/Augmented_reality https://en.wikipedia.org/wiki/Alternate_reality https://en.wikipedia.org/wiki/Multiverse https://en.wikipedia.org/wiki/Virtual_reality https://en.wikipedia.org/wiki/Simulation_hypothesis https://en.wikipedia.org/wiki/Realization_(probability) https://en.wikipedia.org/wiki/Empirical_probability Realization is the art of creating music, typically an accompaniment, from a figured bass, whether by improvisation in real time, or as a detained exercise in writing. It is most commonly associated with Baroque music. https://en.wikipedia.org/wiki/Realization_(figured_bass) Realization, also called Biographie, is a circa 35-metre (115 ft) sport climbing route on a limestone cliff on the southern face of Céüse mountain, near Gap and Sigoyer, in France. After it was first climbed in 2001 by American climber Chris Sharma, it became the first rock climb in the world to have a consensus grade of 9a+ (5.15a).[a] It is considered an historic and important route in rock climbing, and one of the most attempted climbs at its grade.[5][6] https://en.wikipedia.org/wiki/Realization_(climb) In metrology, the realisation of a unit of measure is the conversion of its definition into reality.[1] The International vocabulary of metrology identifies three distinct methods of realisation: Realisation of a measurement unit from its definition. Reproduction of measurement standards. Adopting a particular artefact as a standard. The International Bureau of Weights and Measures maintains the techniques for realisation of the base units in the International System of Units (SI).[2] https://en.wikipedia.org/wiki/Realisation_(metrology) Realized niche width is a phrase relating to ecology, is defined by the actual space that an organism inhabits and the resources it can access as a result of limiting pressures from other species (e.g. superior competitors). An organism's ecological niche is determined by the biotic and abiotic factors that make up that specific ecosystem that allow that specific organism to survive there. The width of an organism's niche is set by the range of conditions a species is able to survive in that specific environment. https://en.wikipedia.org/wiki/Realized_niche_width Realizing Increased Photosynthetic Efficiency (RIPE) is a translational research project that is genetically engineering plants to photosynthesize more efficiently to increase crop yields.[1] RIPE aims to increase agricultural production worldwide, particularly to help reduce hunger and poverty in Sub-Saharan Africa and Southeast Asia by sustainably improving the yield of key food crops including soybeans, rice, cassava[2] and cowpeas.[3] The RIPE project began in 2012, funded by a five-year, $25-million dollar grant from the Bill and Melinda Gates Foundation.[4] In 2017, the project received a $45 million-dollar reinvestment from the Gates Foundation, Foundation for Food and Agriculture Research, and the UK Government's Department for International Development.[5] In 2018, the Gates Foundation contributed an additional $13 million to accelerate the project's progress.[6] https://en.wikipedia.org/wiki/Realizing_Increased_Photosynthetic_Efficiency Realized variance or realised variance (RV, see spelling differences) is the sum of squared returns. For instance the RV can be the sum of squared daily returns for a particular month, which would yield a measure of price variation over this month. More commonly, the realized variance is computed as the sum of squared intraday returns for a particular day. The realized variance is useful because it provides a relatively accurate measure of volatility[1] which is useful for many purposes, including volatility forecasting and forecast evaluation. https://en.wikipedia.org/wiki/Realized_variance The Age of Enlightenment or the Enlightenment,[note 2] also known as the Age of Reason, was an intellectual and philosophical movement that occurred in Europe in the 17th and 18th centuries, with global influences and effects.[2][3] The Enlightenment included a range of ideas centered on the value of human happiness, the pursuit of knowledge obtained by means of reason and the evidence of the senses, and ideals such as natural law, liberty, progress, toleration, fraternity, constitutional government, and separation of church and state.[4][5] https://en.wikipedia.org/wiki/Age_of_Enlightenment https://en.wikipedia.org/wiki/Knowledge Definitions of knowledge try to determine the essential features of knowledge. Closely related terms are conception of knowledge, theory of knowledge, and analysis of knowledge. Some general features of knowledge are widely accepted among philosophers, for example, that it constitutes a cognitive success or an epistemic contact with reality and that propositional knowledge involves true belief. Most definitions of knowledge in analytic philosophy focus on propositional knowledge or knowledge-that, as in knowing that Dave is at home, in contrast to knowledge-how (know-how) expressing practical competence. However, despite the intense study of knowledge in epistemology, the disagreements about its precise nature are still both numerous and deep. Some of those disagreements arise from the fact that different theorists have different goals in mind: some try to provide a practically useful definition by delineating its most salient feature or features, while others aim at a theoretically precise definition of its necessary and sufficient conditions. Further disputes are caused by methodological differences: some theorists start from abstract and general intuitions or hypotheses, others from concrete and specific cases, and still others from linguistic usage. Additional disagreements arise concerning the standards of knowledge: whether knowledge is something rare that demands very high standards, like infallibility, or whether it is something common that requires only the possession of some evidence. One definition that many philosophers consider to be standard, and that has been discussed since ancient Greek philosophy, is justified true belief (JTB). This implies that knowledge is a mental state and that it is not possible to know something false. There is widespread agreement among analytic philosophers that knowledge is a form of true belief. The idea that justification is an additionally required component is due to the intuition that true beliefs based on superstition, lucky guesses, or erroneous reasoning do not constitute knowledge. In this regard, knowledge is more than just being right about something. The source of most disagreements regarding the nature of knowledge concerns what more is needed. According to the standard philosophical definition, it is justification. The original account understands justification internalistically as another mental state of the person, like a perceptual experience, a memory, or a second belief. This additional mental state supports the known proposition and constitutes a reason or evidence for it. However, some modern versions of the standard philosophical definition use an externalistic conception of justification instead. Many such views affirm that a belief is justified if it was produced in the right way, for example, by a reliable cognitive process. The justified-true-belief definition of knowledge came under severe criticism in the second half of the 20th century, mainly due to a series of counterexamples given by Edmund Gettier. Most of these examples aim to illustrate cases in which a justified true belief does not amount to knowledge because its justification is not relevant to its truth. This is often termed epistemic luck since it is just a fortuitous coincidence that the justified belief is also true. A few epistemologists have concluded from these counterexamples that the JTB definition of knowledge is deeply flawed and have sought a radical reconception of knowledge. However, many theorists still agree that the JTB definition is on the right track and have proposed more moderate responses to deal with the suggested counterexamples. Some hold that modifying one's conception of justification is sufficient to avoid them. Another approach is to include an additional requirement besides justification. On this view, being a justified true belief is a necessary but not a sufficient condition of knowledge. A great variety of such criteria has been suggested. They usually manage to avoid many of the known counterexamples but they often fall prey to newly proposed cases. It has been argued that, in order to circumvent all Gettier cases, the additional criterion needs to exclude epistemic luck altogether. However, this may require the stipulation of a very high standard of knowledge: that nothing less than infallibility is needed to exclude all forms of luck. The defeasibility theory of knowledge is one example of a definition based on a fourth criterion besides justified true belief. The additional requirement is that there is no truth that would constitute a defeating reason of the belief if the person knew about it. Other alternatives to the JTB definition are reliabilism, which holds that knowledge has to be produced by reliable processes, causal theories, which require that the known fact caused the knowledge, and virtue theories, which identify knowledge with the manifestation of intellectual virtues. Not all forms of knowledge are propositional, and various definitions of different forms of non-propositional knowledge have also been proposed. But among analytic philosophers this field of inquiry is less active and characterized by less controversy. Someone has practical knowledge or know-how if they possess the corresponding competence or ability. Knowledge by acquaintance constitutes a relation not to a proposition but to an object. It is defined as familiarity with its object based on direct perceptual experience of it. https://en.wikipedia.org/wiki/Definitions_of_knowledge Knowledge transfer is the sharing or disseminating of knowledge and the providing of inputs to problem solving.[1] In organizational theory, knowledge transfer is the practical problem of transferring knowledge from one part of the organization to another. Like knowledge management, knowledge transfer seeks to organize, create, capture or distribute knowledge and ensure its availability for future users. It is considered to be more than just a communication problem. If it were merely that, then a memorandum, an e-mail or a meeting would accomplish the knowledge transfer. Knowledge transfer is more complex because: knowledge resides in organizational members, tools, tasks, and their subnetworks[2] and much knowledge in organizations is tacit or hard to articulate.[3] The subject has been taken up under the title of knowledge management since the 1990s. The term has also been applied to the transfer of knowledge at the international level.[4][5] In business, knowledge transfer now has become a common topic in mergers and acquisitions.[6] It focuses on transferring technological platform, market experience, managerial expertise, corporate culture, and other intellectual capital that can improve the companies' competence.[7] Since technical skills and knowledge are very important assets for firms' competence in the global competition,[8] unsuccessful knowledge transfer can have a negative impact on corporations and lead to the expensive and time-consuming M&A not creating values to the firms.[9] https://en.wikipedia.org/wiki/Knowledge_transfer Knowledge extraction is the creation of knowledge from structured (relational databases, XML) and unstructured (text, documents, images) sources. The resulting knowledge needs to be in a machine-readable and machine-interpretable format and must represent knowledge in a manner that facilitates inferencing. Although it is methodically similar to information extraction (NLP) and ETL (data warehouse), the main criterion is that the extraction result goes beyond the creation of structured information or the transformation into a relational schema. It requires either the reuse of existing formal knowledge (reusing identifiers or ontologies) or the generation of a schema based on the source data. The RDB2RDF W3C group [1] is currently standardizing a language for extraction of resource description frameworks (RDF) from relational databases. Another popular example for knowledge extraction is the transformation of Wikipedia into structured data and also the mapping to existing knowledge (see DBpedia and Freebase). https://en.wikipedia.org/wiki/Knowledge_extraction In philosophy, a distinction is often made between two different kinds of knowledge: knowledge by acquaintance and knowledge by description. Whereas knowledge by description is something like ordinary propositional knowledge (e.g. "I know that snow is white"), knowledge by acquaintance is familiarity with a person, place, or thing, typically obtained through perceptual experience (e.g. "I know Sam", "I know the city of Bogotá", or "I know Russell's Problems of Philosophy").[1] According to Bertrand Russell's classic account of acquaintance knowledge, acquaintance is a direct causal interaction between a person and some object that the person is perceiving. https://en.wikipedia.org/wiki/Knowledge_by_acquaintance The knowledge economy (or the knowledge-based economy) is an economic system in which the production of goods and services is based principally on knowledge-intensive activities that contribute to advancement in technical and scientific innovation.[1] The key element of value is the greater dependence on human capital and intellectual property for the source of the innovative ideas, information and practices.[2] Organisations are required to capitalise this "knowledge" into their production to stimulate and deepen the business development process. There is less reliance on physical input and natural resources. A knowledge-based economy relies on the crucial role of intangible assets within the organisations' settings in facilitating modern economic growth.[3] https://en.wikipedia.org/wiki/Knowledge_economy The knowledge argument (also known as Mary's Room or Mary the super-scientist) is a philosophical thought experiment proposed by Frank Jackson in his article "Epiphenomenal Qualia" (1982) and extended in "What Mary Didn't Know" (1986). The experiment describes Mary, a scientist who exists in a black-and-white world where she has extensive access to physical descriptions of color, but no actual perceptual experience of color. Mary has learned everything there is to learn about color, but she has never actually experienced it for herself. The central question of the thought experiment is whether Mary will gain new knowledge when she goes outside the colorless world and experiences seeing in color https://en.wikipedia.org/wiki/Knowledge_argument Knowledge management (KM) is the collection of methods relating to creating, sharing, using and managing the knowledge and information of an organization.[1] It refers to a multidisciplinary approach to achieve organizational objectives by making the best use of knowledge.[2] https://en.wikipedia.org/wiki/Knowledge_management Embedding of a knowledge graph. The vector representation of the entities and relations can be used for different machine learning applications. In representation learning, knowledge graph embedding (KGE), also referred to as knowledge representation learning (KRL), or multi-relation learning,[1] is a machine learning task of learning a low-dimensional representation of a knowledge graph's entities and relations while preserving their semantic meaning.[1][2][3] Leveraging their embedded representation, knowledge graphs (KGs) can be used for various applications such as link prediction, triple classification, entity recognition, clustering, and relation extraction.[1][4] https://en.wikipedia.org/wiki/Knowledge_graph_embedding A relationship extraction task requires the detection and classification of semantic relationship mentions within a set of artifacts, typically from text or XML documents. The task is very similar to that of information extraction (IE), but IE additionally requires the removal of repeated relations (disambiguation) and generally refers to the extraction of many different relationships. https://en.wikipedia.org/wiki/Relationship_extraction A document is a written, drawn, presented, or memorialized representation of thought, often the manifestation of non-fictional, as well as fictional, content. The word originates from the Latin Documentum, which denotes a "teaching" or "lesson": the verb doceō denotes "to teach". In the past, the word was usually used to denote written proof useful as evidence of a truth or fact. In the Computer Age, "document" usually denotes a primarily textual computer file, including its structure and format, e.g. fonts, colors, and images. Contemporarily, "document" is not defined by its transmission medium, e.g., paper, given the existence of electronic documents. "Documentation" is distinct because it has more denotations than "document". Documents are also distinguished from "realia", which are three-dimensional objects that would otherwise satisfy the definition of "document" because they memorialize or represent thought; documents are considered more as 2-dimensional representations. While documents can have large varieties of customization, all documents can be shared freely and have the right to do so, creativity can be represented by documents, also. History, events, examples, opinions, etc. all can be expressed in documents. https://en.wikipedia.org/wiki/Document In library classification systems, realia are three-dimensional objects from real life such as coins, tools, and textiles, that do not fit into the traditional categories of library material. They can be either man-made (artifacts, tools, utensils, etc.) or naturally occurring (specimens, samples, etc.), usually borrowed, purchased, or received as donation by a teacher, library, or museum for use in classroom instruction or in exhibits. Archival and manuscript collections often receive items of memorabilia such as badges, emblems, insignias, jewelry, leather goods, needlework, etc., in connection with gifts of personal papers. Most government or institutional archives reject gifts of non-documentary objects unless they have a documentary value. When accepting large bequests of mixed objects they normally have the donors sign legal documents giving permission to the archive to destroy, exchange, sell, or dispose in any way those objects which, according to the best judgement of the archivist, are not manuscripts (which can include typescripts or printouts) or are not immediately useful for understanding the manuscripts. Recently, the usage of this term has been criticized by librarians based on the usage of term realia to refer to artistic and historical artifacts and objects, and suggesting the use of the phrase "real world object" to describe the broader categories of three-dimensional objects in libraries. https://en.wikipedia.org/wiki/Realia_(library_science) https://en.wikipedia.org/wiki/Knowledge_Web https://en.wikipedia.org/wiki/Commonsense_knowledge_(artificial_intelligence) https://en.wikipedia.org/wiki/Zero_knowledge https://en.wikipedia.org/wiki/Knowledge_Network https://en.wikipedia.org/wiki/Tacit_knowledge https://en.wikipedia.org/wiki/Procedural_knowledge https://en.wikipedia.org/wiki/The_Archaeology_of_Knowledge https://en.wikipedia.org/wiki/Knowledge_distillation https://en.wikipedia.org/wiki/Definitions_of_knowledge https://en.wikipedia.org/wiki/Knowledge_representation_and_reasoning https://en.wikipedia.org/wiki/Divine_knowledge https://en.wikipedia.org/wiki/Curse_of_knowledge https://en.wikipedia.org/wiki/Decolonization_of_knowledge https://en.wikipedia.org/wiki/Science https://en.wikipedia.org/wiki/Word_of_Knowledge https://en.wikipedia.org/wiki/Knowledge_base https://en.wikipedia.org/wiki/Encyclopedia https://en.wikipedia.org/wiki/Desacralization_of_knowledge https://en.wikipedia.org/wiki/Meta-knowledge https://en.wikipedia.org/wiki/Metacognition#Metastrategic_knowledge https://en.wikipedia.org/wiki/Core_Knowledge_Foundation https://en.wikipedia.org/wiki/Western_esotericism https://en.wikipedia.org/wiki/Dangerous_Knowledge https://en.wikipedia.org/wiki/Coloniality_of_knowledge https://en.wikipedia.org/wiki/Gettier_problem https://en.wikipedia.org/wiki/Artificial_intelligence#Knowledge_representation https://en.wikipedia.org/wiki/Ontology_language#Classification_of_ontology_languages https://en.wikipedia.org/wiki/Academic_discipline https://en.wikipedia.org/wiki/Forbidden_fruit https://en.wikipedia.org/wiki/Knowledge,_Skills,_and_Abilities https://en.wikipedia.org/wiki/Knowledge_Navigator https://en.wikipedia.org/wiki/Knowledge_and_Its_Limits https://en.wikipedia.org/wiki/Monopolies_of_knowledge https://en.wikipedia.org/wiki/Knowledge_(legal_construct) https://en.wikipedia.org/wiki/Empirical_evidence https://en.wikipedia.org/wiki/Self-knowledge https://en.wikipedia.org/wiki/Tree_of_the_knowledge_of_good_and_evil https://en.wikipedia.org/wiki/Knowledge_acquisition https://en.wikipedia.org/wiki/Open_knowledge https://en.wikipedia.org/wiki/Book_of_Knowledge https://en.wikipedia.org/wiki/Taxes_on_knowledge https://en.wikipedia.org/wiki/General_knowledge https://en.wikipedia.org/wiki/Zero-knowledge_proof From Wikipedia, the free encyclopedia "ZKP" redirects here. For the airport in Russia, see Zyryanka Airport. For other uses, see Zero knowledge. In cryptography, a zero-knowledge proof or zero-knowledge protocol is a method by which one party (the prover) can prove to another party (the verifier) that a given statement is true while the prover avoids conveying any additional information apart from the fact that the statement is indeed true. The essence of zero-knowledge proofs is that it is trivial to prove that one possesses knowledge of certain information by simply revealing it; the challenge is to prove such possession without revealing the information itself or any additional information.[1] If proving a statement requires that the prover possess some secret information, then the verifier will not be able to prove the statement to anyone else without possessing the secret information. The statement being proved must include the assertion that the prover has such knowledge, but without including or transmitting the knowledge itself in the assertion. Otherwise, the statement would not be proved in zero-knowledge because it provides the verifier with additional information about the statement by the end of the protocol. A zero-knowledge proof of knowledge is a special case when the statement consists only of the fact that the prover possesses the secret information. Interactive zero-knowledge proofs require interaction between the individual (or computer system) proving their knowledge and the individual validating the proof.[1] This section needs to be updated. The reason given is: There are also Non-interactive zero-knowledge proofs. Please help update this article to reflect recent events or newly available information. (December 2022) A protocol implementing zero-knowledge proofs of knowledge must necessarily require interactive input from the verifier. This interactive input is usually in the form of one or more challenges such that the responses from the prover will convince the verifier if and only if the statement is true, i.e., if the prover does possess the claimed knowledge. If this were not the case, the verifier could record the execution of the protocol and replay it to convince someone else that they possess the secret information. The new party's acceptance is either justified since the replayer does possess the information (which implies that the protocol leaked information, and thus, is not proved in zero-knowledge), or the acceptance is spurious, i.e., was accepted from someone who does not actually possess the information. Some forms of non-interactive zero-knowledge proofs exist,[2][3] but the validity of the proof relies on computational assumptions (typically the assumptions of an ideal cryptographic hash function). Abstract examples The Ali Baba cave Peggy randomly takes either path A or B, while Victor waits outside Victor chooses an exit path Peggy reliably appears at the exit Victor names There is a well-known story presenting the fundamental ideas of zero-knowledge proofs, first published in 1990 by Jean-Jacques Quisquater and others in their paper "How to Explain Zero-Knowledge Protocols to Your Children".[4] Using the common Alice and Bob anthropomorphic thought experiment placeholders, the two parties in a zero-knowledge proof are Peggy as the prover of the statement, and Victor, the verifier of the statement. In this story, Peggy has uncovered the secret word used to open a magic door in a cave. The cave is shaped like a ring, with the entrance on one side and the magic door blocking the opposite side. Victor wants to know whether Peggy knows the secret word; but Peggy, being a very private person, does not want to reveal her knowledge (the secret word) to Victor or to reveal the fact of her knowledge to the world in general. They label the left and right paths from the entrance A and B. First, Victor waits outside the cave as Peggy goes in. Peggy takes either path A or B; Victor is not allowed to see which path she takes. Then, Victor enters the cave and shouts the name of the path he wants her to use to return, either A or B, chosen at random. Providing she really does know the magic word, this is easy: she opens the door, if necessary, and returns along the desired path. However, suppose she did not know the word. Then, she would only be able to return by the named path if Victor were to give the name of the same path by which she had entered. Since Victor would choose A or B at random, she would have a 50% chance of guessing correctly. If they were to repeat this trick many times, say 20 times in a row, her chance of successfully anticipating all of Victor's requests would become very small (1 in 220, or very roughly 1 in a million). Thus, if Peggy repeatedly appears at the exit Victor names, he can conclude that it is extremely probable that Peggy does, in fact, know the secret word. One side note with respect to third-party observers: even if Victor is wearing a hidden camera that records the whole transaction, the only thing the camera will record is in one case Victor shouting "A!" and Peggy appearing at A or in the other case Victor shouting "B!" and Peggy appearing at B. A recording of this type would be trivial for any two people to fake (requiring only that Peggy and Victor agree beforehand on the sequence of A's and B's that Victor will shout). Such a recording will certainly never be convincing to anyone but the original participants. In fact, even a person who was present as an observer at the original experiment would be unconvinced, since Victor and Peggy might have orchestrated the whole "experiment" from start to finish. Further notice that if Victor chooses his A's and B's by flipping a coin on-camera, this protocol loses its zero-knowledge property; the on-camera coin flip would probably be convincing to any person watching the recording later. Thus, although this does not reveal the secret word to Victor, it does make it possible for Victor to convince the world in general that Peggy has that knowledge—counter to Peggy's stated wishes. However, digital cryptography generally "flips coins" by relying on a pseudo-random number generator, which is akin to a coin with a fixed pattern of heads and tails known only to the coin's owner. If Victor's coin behaved this way, then again it would be possible for Victor and Peggy to have faked the "experiment", so using a pseudo-random number generator would not reveal Peggy's knowledge to the world in the same way that using a flipped coin would. Notice that Peggy could prove to Victor that she knows the magic word, without revealing it to him, in a single trial. If both Victor and Peggy go together to the mouth of the cave, Victor can watch Peggy go in through A and come out through B. This would prove with certainty that Peggy knows the magic word, without revealing the magic word to Victor. However, such a proof could be observed by a third party, or recorded by Victor and such a proof would be convincing to anybody. In other words, Peggy could not refute such proof by claiming she colluded with Victor, and she is therefore no longer in control of who is aware of her knowledge. Two balls and the colour-blind friend Imagine your friend "Victor" is red-green colour-blind (while you are not) and you have two balls: one red and one green, but otherwise identical. To Victor, the balls seem completely identical. Victor is skeptical that the balls are actually distinguishable. You want to prove to Victor that the balls are in fact differently-coloured, but nothing else. In particular, you do not want to reveal which ball is the red one and which is the green. Here is the proof system. You give the two balls to Victor and he puts them behind his back. Next, he takes one of the balls and brings it out from behind his back and displays it. He then places it behind his back again and then chooses to reveal just one of the two balls, picking one of the two at random with equal probability. He will ask you, "Did I switch the ball?" This whole procedure is then repeated as often as necessary. By looking at the balls' colours, you can, of course, say with certainty whether or not he switched them. On the other hand, if the balls were the same colour and hence indistinguishable, there is no way you could guess correctly with probability higher than 50%. Since the probability that you would have randomly succeeded at identifying each switch/non-switch is 50%, the probability of having randomly succeeded at all switch/non-switches approaches zero ("soundness"). If you and your friend repeat this "proof" multiple times (e.g. 20 times), your friend should become convinced ("completeness") that the balls are indeed differently coloured. The above proof is zero-knowledge because your friend never learns which ball is green and which is red; indeed, he gains no knowledge about how to distinguish the balls.[5] Definition This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources in this section. Unsourced material may be challenged and removed. Find sources: "Zero-knowledge proof" – news · newspapers · books · scholar · JSTOR (July 2022) (Learn how and when to remove this template message) A zero-knowledge proof of some statement must satisfy three properties: Completeness: if the statement is true, an honest verifier (that is, one following the protocol properly) will be convinced of this fact by an honest prover. Soundness: if the statement is false, no cheating prover can convince an honest verifier that it is true, except with some small probability. Zero-knowledge: if the statement is true, no verifier learns anything other than the fact that the statement is true. In other words, just knowing the statement (not the secret) is sufficient to imagine a scenario showing that the prover knows the secret. This is formalized by showing that every verifier has some simulator that, given only the statement to be proved (and no access to the prover), can produce a transcript that "looks like" an interaction between an honest prover and the verifier in question. The first two of these are properties of more general interactive proof systems. The third is what makes the proof zero-knowledge.[6] Zero-knowledge proofs are not proofs in the mathematical sense of the term because there is some small probability, the soundness error, that a cheating prover will be able to convince the verifier of a false statement. In other words, zero-knowledge proofs are probabilistic "proofs" rather than deterministic proofs. However, there are techniques to decrease the soundness error to negligibly small values (e.g. guessing correctly on a hundred or thousand binary decisions has a 1 / 2^100 or 1/ 2^1000 soundness error, respectively. As the number of bits increases, soundness error decreases toward zero). A formal definition of zero-knowledge has to use some computational model, the most common one being that of a Turing machine. Let P P, V V, and S S be Turing machines. An interactive proof system with ( P , V ) {\displaystyle (P,V)} for a language L L is zero-knowledge if for any probabilistic polynomial time (PPT) verifier V ^ {\hat {V}} there exists a PPT simulator S S such that ∀ x ∈ L , z ∈ { 0 , 1 } ∗ , View V ^ ⁡ [ P ( x ) ↔ V ^ ( x , z ) ] = S ( x , z ) {\displaystyle \forall x\in L,z\in \{0,1\}^{*},\operatorname {View} _{\hat {V}}\left[P(x)\leftrightarrow {\hat {V}}(x,z)\right]=S(x,z)} where View V ^ ⁡ [ P ( x ) ↔ V ^ ( x , z ) ] {\displaystyle \operatorname {View} _{\hat {V}}\left[P(x)\leftrightarrow {\hat {V}}(x,z)\right]} is a record of the interactions between P ( x ) P(x) and V ^ ( x , z ) {\displaystyle {\hat {V}}(x,z)}. The prover P P is modeled as having unlimited computation power (in practice, P P usually is a probabilistic Turing machine). Intuitively, the definition states that an interactive proof system ( P , V ) {\displaystyle (P,V)} is zero-knowledge if for any verifier V ^ {\hat {V}} there exists an efficient simulator S S (depending on V ^ {\hat {V}}) that can reproduce the conversation between P P and V ^ {\hat {V}} on any given input. The auxiliary string z z in the definition plays the role of "prior knowledge" (including the random coins of V ^ {\hat {V}}). The definition implies that V ^ {\hat {V}} cannot use any prior knowledge string z z to mine information out of its conversation with P P, because if S S is also given this prior knowledge then it can reproduce the conversation between V ^ {\hat {V}} and P P just as before.[citation needed] The definition given is that of perfect zero-knowledge. Computational zero-knowledge is obtained by requiring that the views of the verifier V ^ {\hat {V}} and the simulator are only computationally indistinguishable, given the auxiliary string.[citation needed] Practical examples Discrete log of a given value We can apply these ideas to a more realistic cryptography application. Peggy wants to prove to Victor that she knows the discrete log of a given value in a given group.[7] For example, given a value y y, a large prime p p and a generator g g, she wants to prove that she knows a value x x such that g x mod p = y {\displaystyle g^{x}{\bmod {p}}=y}, without revealing x x. Indeed, knowledge of x x could be used as a proof of identity, in that Peggy could have such knowledge because she chose a random value x x that she didn't reveal to anyone, computed y = g x mod p {\displaystyle y=g^{x}{\bmod {p}}} and distributed the value of y y to all potential verifiers, such that at a later time, proving knowledge of x x is equivalent to proving identity as Peggy. The protocol proceeds as follows: in each round, Peggy generates a random number r r, computes C = g r mod p {\displaystyle C=g^{r}{\bmod {p}}} and discloses this to Victor. After receiving C C, Victor randomly issues one of the following two requests: he either requests that Peggy discloses the value of r r, or the value of ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}}. With either answer, Peggy is only disclosing a random value, so no information is disclosed by a correct execution of one round of the protocol. Victor can verify either answer; if he requested r r, he can then compute g r mod p {\displaystyle g^{r}{\bmod {p}}} and verify that it matches C C. If he requested ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}}, he can verify that C C is consistent with this, by computing g ( x + r ) mod ( p − 1 ) mod p {\displaystyle g^{(x+r){\bmod {(p-1)}}}{\bmod {p}}} and verifying that it matches ( C ⋅ y ) mod p {\displaystyle (C\cdot y){\bmod {p}}}. If Peggy indeed knows the value of x x, she can respond to either one of Victor's possible challenges. If Peggy knew or could guess which challenge Victor is going to issue, then she could easily cheat and convince Victor that she knows x x when she does not: if she knows that Victor is going to request r r, then she proceeds normally: she picks r r, computes C = g r mod p {\displaystyle C=g^{r}{\bmod {p}}} and discloses C C to Victor; she will be able to respond to Victor's challenge. On the other hand, if she knows that Victor will request ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}}, then she picks a random value r ′ r', computes C ′ = g r ′ ⋅ ( g x ) − 1 mod p {\displaystyle C'=g^{r'}\cdot \left(g^{x}\right)^{-1}{\bmod {p}}}, and discloses C ′ C' to Victor as the value of C C that he is expecting. When Victor challenges her to reveal ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}}, she reveals r ′ r', for which Victor will verify consistency, since he will in turn compute g r ′ mod p {\displaystyle g^{r'}{\bmod {p}}}, which matches C ′ ⋅ y C'\cdot y, since Peggy multiplied by the modular multiplicative inverse of y y. However, if in either one of the above scenarios Victor issues a challenge other than the one she was expecting and for which she manufactured the result, then she will be unable to respond to the challenge under the assumption of infeasibility of solving the discrete log for this group. If she picked r r and disclosed C = g r mod p {\displaystyle C=g^{r}{\bmod {p}}}, then she will be unable to produce a valid ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}} that would pass Victor's verification, given that she does not know x x. And if she picked a value r ′ r' that poses as ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}}, then she would have to respond with the discrete log of the value that she disclosed – but Peggy does not know this discrete log, since the value C she disclosed was obtained through arithmetic with known values, and not by computing a power with a known exponent. Thus, a cheating prover has a 0.5 probability of successfully cheating in one round. By executing a large enough number of rounds, the probability of a cheating prover succeeding can be made arbitrarily low. Short summary Peggy proves to know the value of x (for example her password). Peggy and Victor agree on a prime p p and a generator g g of the multiplicative group of the field Z p {\displaystyle \mathbb {Z} _{p}}. Peggy calculates the value y = g x mod p {\displaystyle y=g^{x}{\bmod {p}}} and transfers the value to Victor. The following two steps are repeated a (large) number of times. Peggy repeatedly picks a random value r ∈ U [ 0 , p − 2 ] {\displaystyle r\in U[0,p-2]} and calculates C = g r mod p {\displaystyle C=g^{r}{\bmod {p}}}. She transfers the value C C to Victor. Victor asks Peggy to calculate and transfer either the value ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}} or the value r r. In the first case Victor verifies ( C ⋅ y ) mod p ≡ g ( x + r ) mod ( p − 1 ) mod p {\displaystyle (C\cdot y){\bmod {p}}\equiv g^{(x+r){\bmod {(p-1)}}}{\bmod {p}}}. In the second case he verifies C ≡ g r mod p {\displaystyle C\equiv g^{r}{\bmod {p}}}. The value ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(}}p-1)} can be seen as the encrypted value of x mod ( p − 1 ) {\displaystyle x{\bmod {(}}p-1)}. If r r is truly random, equally distributed between zero and ( p − 2 ) {\displaystyle (p-2)}, this does not leak any information about x x (see one-time pad). Hamiltonian cycle for a large graph The following scheme is due to Manuel Blum.[8] In this scenario, Peggy knows a Hamiltonian cycle for a large graph G. Victor knows G but not the cycle (e.g., Peggy has generated G and revealed it to him.) Finding a Hamiltonian cycle given a large graph is believed to be computationally infeasible, since its corresponding decision version is known to be NP-complete. Peggy will prove that she knows the cycle without simply revealing it (perhaps Victor is interested in buying it but wants verification first, or maybe Peggy is the only one who knows this information and is proving her identity to Victor). To show that Peggy knows this Hamiltonian cycle, she and Victor play several rounds of a game. At the beginning of each round, Peggy creates H, a graph which is isomorphic to G (i.e. H is just like G except that all the vertices have different names). Since it is trivial to translate a Hamiltonian cycle between isomorphic graphs with known isomorphism, if Peggy knows a Hamiltonian cycle for G she also must know one for H. Peggy commits to H. She could do so by using a cryptographic commitment scheme. Alternatively, she could number the vertices of H. Next, for each edge of H, on a small piece of paper, she writes down the two vertices that the edge joins. Then she puts all these pieces of paper face down on a table. The purpose of this commitment is that Peggy is not able to change H while, at the same time, Victor has no information about H. Victor then randomly chooses one of two questions to ask Peggy. He can either ask her to show the isomorphism between H and G (see graph isomorphism problem), or he can ask her to show a Hamiltonian cycle in H. If Peggy is asked to show that the two graphs are isomorphic, she first uncovers all of H (e.g. by turning over all pieces of papers that she put on the table) and then provides the vertex translations that map G to H. Victor can verify that they are indeed isomorphic. If Peggy is asked to prove that she knows a Hamiltonian cycle in H, she translates her Hamiltonian cycle in G onto H and only uncovers the edges on the Hamiltonian cycle. This is enough for Victor to check that H does indeed contain a Hamiltonian cycle. It is important that the commitment to the graph be such that Victor can verify, in the second case, that the cycle is really made of edges from H. This can be done by, for example, committing to every edge (or lack thereof) separately. Completeness If Peggy does know a Hamiltonian cycle in G, she can easily satisfy Victor's demand for either the graph isomorphism producing H from G (which she had committed to in the first step) or a Hamiltonian cycle in H (which she can construct by applying the isomorphism to the cycle in G). Zero-knowledge Peggy's answers do not reveal the original Hamiltonian cycle in G. Each round, Victor will learn only H's isomorphism to G or a Hamiltonian cycle in H. He would need both answers for a single H to discover the cycle in G, so the information remains unknown as long as Peggy can generate a distinct H every round. If Peggy does not know of a Hamiltonian cycle in G, but somehow knew in advance what Victor would ask to see each round then she could cheat. For example, if Peggy knew ahead of time that Victor would ask to see the Hamiltonian cycle in H then she could generate a Hamiltonian cycle for an unrelated graph. Similarly, if Peggy knew in advance that Victor would ask to see the isomorphism then she could simply generate an isomorphic graph H (in which she also does not know a Hamiltonian cycle). Victor could simulate the protocol by himself (without Peggy) because he knows what he will ask to see. Therefore, Victor gains no information about the Hamiltonian cycle in G from the information revealed in each round. Soundness If Peggy does not know the information, she can guess which question Victor will ask and generate either a graph isomorphic to G or a Hamiltonian cycle for an unrelated graph, but since she does not know a Hamiltonian cycle for G she cannot do both. With this guesswork, her chance of fooling Victor is 2−n, where n is the number of rounds. For all realistic purposes, it is infeasibly difficult to defeat a zero-knowledge proof with a reasonable number of rounds in this way. Variants of zero-knowledge Different variants of zero-knowledge can be defined by formalizing the intuitive concept of what is meant by the output of the simulator "looking like" the execution of the real proof protocol in the following ways: We speak of perfect zero-knowledge if the distributions produced by the simulator and the proof protocol are distributed exactly the same. This is for instance the case in the first example above. Statistical zero-knowledge[9] means that the distributions are not necessarily exactly the same, but they are statistically close, meaning that their statistical difference is a negligible function. We speak of computational zero-knowledge if no efficient algorithm can distinguish the two distributions. Zero knowledge types Proof of knowledge: the knowledge is hidden in the exponent like in the example shown above. Pairing based cryptography: given f(x) and f(y), without knowing x and y, it is possible to compute f(x×y). Witness indistinguishable proof: verifiers cannot know which witness is used for producing the proof. Multi-party computation: while each party can keep their respective secret, they together produce a result. Ring signature: outsiders have no idea which key is used for signing. Applications Authentication systems Research in zero-knowledge proofs has been motivated by authentication systems where one party wants to prove its identity to a second party via some secret information (such as a password) but doesn't want the second party to learn anything about this secret. This is called a "zero-knowledge proof of knowledge". However, a password is typically too small or insufficiently random to be used in many schemes for zero-knowledge proofs of knowledge. A zero-knowledge password proof is a special kind of zero-knowledge proof of knowledge that addresses the limited size of passwords.[citation needed] In April 2015, the Sigma protocol (one-out-of-many proofs) was introduced.[10] In August 2021, Cloudflare, an American web infrastructure and security company decided to use the one-out-of-many proofs mechanism for private web verification using vendor hardware.[11] Ethical behavior One of the uses of zero-knowledge proofs within cryptographic protocols is to enforce honest behavior while maintaining privacy. Roughly, the idea is to force a user to prove, using a zero-knowledge proof, that its behavior is correct according to the protocol.[12][13] Because of soundness, we know that the user must really act honestly in order to be able to provide a valid proof. Because of zero knowledge, we know that the user does not compromise the privacy of its secrets in the process of providing the proof.[citation needed] Nuclear disarmament In 2016, the Princeton Plasma Physics Laboratory and Princeton University demonstrated a technique that may have applicability to future nuclear disarmament talks. It would allow inspectors to confirm whether or not an object is indeed a nuclear weapon without recording, sharing or revealing the internal workings which might be secret.[14] Blockchains Zero-knowledge proofs were applied in the Zerocoin and Zerocash protocols, which culminated in the birth of Zcoin[15] (later rebranded as Firo in 2020)[16] and Zcash cryptocurrencies in 2016. Zerocoin has a built-in mixing model that does not trust any peers or centralised mixing providers to ensure anonymity.[15] Users can transact in a base currency and can cycle the currency into and out of Zerocoins.[17] The Zerocash protocol uses a similar model (a variant known as a non-interactive zero-knowledge proof)[18] except that it can obscure the transaction amount, while Zerocoin cannot. Given significant restrictions of transaction data on the Zerocash network, Zerocash is less prone to privacy timing attacks when compared to Zerocoin. However, this additional layer of privacy can cause potentially undetected hyperinflation of Zerocash supply because fraudulent coins cannot be tracked.[15][19] In 2018, Bulletproofs were introduced. Bulletproofs are an improvement from non-interactive zero-knowledge proof where trusted setup is not needed.[20] It was later implemented into the Mimblewimble protocol (which the Grin and Beam cryptocurrencies are based upon) and Monero cryptocurrency.[21] In 2019, Firo implemented the Sigma protocol, which is an improvement on the Zerocoin protocol without trusted setup.[22][10] In the same year, Firo introduced the Lelantus protocol, an improvement on the Sigma protocol, where the former hides the origin and amount of a transaction.[23] History Zero-knowledge proofs were first conceived in 1985 by Shafi Goldwasser, Silvio Micali, and Charles Rackoff in their paper "The Knowledge Complexity of Interactive Proof-Systems".[12] This paper introduced the IP hierarchy of interactive proof systems (see interactive proof system) and conceived the concept of knowledge complexity, a measurement of the amount of knowledge about the proof transferred from the prover to the verifier. They also gave the first zero-knowledge proof for a concrete problem, that of deciding quadratic nonresidues mod m. Together with a paper by László Babai and Shlomo Moran, this landmark paper invented interactive proof systems, for which all five authors won the first Gödel Prize in 1993. In their own words, Goldwasser, Micali, and Rackoff say: Of particular interest is the case where this additional knowledge is essentially 0 and we show that [it] is possible to interactively prove that a number is quadratic non residue mod m releasing 0 additional knowledge. This is surprising as no efficient algorithm for deciding quadratic residuosity mod m is known when m’s factorization is not given. Moreover, all known NP proofs for this problem exhibit the prime factorization of m. This indicates that adding interaction to the proving process, may decrease the amount of knowledge that must be communicated in order to prove a theorem. The quadratic nonresidue problem has both an NP and a co-NP algorithm, and so lies in the intersection of NP and co-NP. This was also true of several other problems for which zero-knowledge proofs were subsequently discovered, such as an unpublished proof system by Oded Goldreich verifying that a two-prime modulus is not a Blum integer.[24] Oded Goldreich, Silvio Micali, and Avi Wigderson took this one step further, showing that, assuming the existence of unbreakable encryption, one can create a zero-knowledge proof system for the NP-complete graph coloring problem with three colors. Since every problem in NP can be efficiently reduced to this problem, this means that, under this assumption, all problems in NP have zero-knowledge proofs.[25] The reason for the assumption is that, as in the above example, their protocols require encryption. A commonly cited sufficient condition for the existence of unbreakable encryption is the existence of one-way functions, but it is conceivable that some physical means might also achieve it. On top of this, they also showed that the graph nonisomorphism problem, the complement of the graph isomorphism problem, has a zero-knowledge proof. This problem is in co-NP, but is not currently known to be in either NP or any practical class. More generally, Russell Impagliazzo and Moti Yung as well as Ben-Or et al. would go on to show that, also assuming one-way functions or unbreakable encryption, that there are zero-knowledge proofs for all problems in IP = PSPACE, or in other words, anything that can be proved by an interactive proof system can be proved with zero knowledge.[26][27] Not liking to make unnecessary assumptions, many theorists sought a way to eliminate the necessity of one way functions. One way this was done was with multi-prover interactive proof systems (see interactive proof system), which have multiple independent provers instead of only one, allowing the verifier to "cross-examine" the provers in isolation to avoid being misled. It can be shown that, without any intractability assumptions, all languages in NP have zero-knowledge proofs in such a system.[28] It turns out that in an Internet-like setting, where multiple protocols may be executed concurrently, building zero-knowledge proofs is more challenging. The line of research investigating concurrent zero-knowledge proofs was initiated by the work of Dwork, Naor, and Sahai.[29] One particular development along these lines has been the development of witness-indistinguishable proof protocols. The property of witness-indistinguishability is related to that of zero-knowledge, yet witness-indistinguishable protocols do not suffer from the same problems of concurrent execution.[30] Another variant of zero-knowledge proofs are non-interactive zero-knowledge proofs. Blum, Feldman, and Micali showed that a common random string shared between the prover and the verifier is enough to achieve computational zero-knowledge without requiring interaction.[2][3] Zero-Knowledge Proof protocols The most popular interactive or non-interactive zero-knowledge proof (e.g., zk-SNARK) protocols can be broadly categorized in the following four categories: Succinct Non-Interactive ARguments of Knowledge (SNARK), Scalable Transparent ARgument of Knowledge (STARK), Verifiable Polynomial Delegation (VPD), and Succinct Non-interactive ARGuments (SNARG). A list of zero-knowledge proof protocols and libraries is provided below along with comparisons based on transparency, universality, plausible post-quantum security, and programming paradigm.[31] A transparent protocol is one that does not require any trusted setup and uses public randomness. A universal protocol is one that does not require a separate trusted setup for each circuit. Finally, a plausibly post-quantum protocol is one that is not susceptible to known attacks involving quantum algorithms. Zero-knowledge proof (ZKP) systems ZKP System Publication year Protocol Transparent Universal Plausibly Post-Quantum Secure Programming Paradigm Pinocchio[32] 2013 zk-SNARK No No No Procedural Geppetto[33] 2015 zk-SNARK No No No Procedural TinyRAM[34] 2013 zk-SNARK No No No Procedural Buffet[35] 2015 zk-SNARK No No No Procedural ZoKrates[36] 2018 zk-SNARK No No No Procedural xJsnark[37] 2018 zk-SNARK No No No Procedural vRAM[38] 2018 zk-SNARG No Yes No Assembly vnTinyRAM[39] 2014 zk-SNARK No Yes No Procedural MIRAGE[40] 2020 zk-SNARK No Yes No Arithmetic Circuits Sonic[41] 2019 zk-SNARK No Yes No Arithmetic Circuits Marlin[42] 2020 zk-SNARK No Yes No Arithmetic Circuits PLONK[43] 2019 zk-SNARK No Yes No Arithmetic Circuits SuperSonic[44] 2020 zk-SNARK Yes Yes No Arithmetic Circuits Bulletproofs[20] 2018 Bulletproofs Yes Yes No Arithmetic Circuits Hyrax[45] 2018 zk-SNARK Yes Yes No Arithmetic Circuits Halo[46] 2019 zk-SNARK Yes Yes No Arithmetic Circuits Virgo[47] 2020 zk-SNARK Yes Yes Yes Arithmetic Circuits Ligero[48] 2017 zk-SNARK Yes Yes Yes Arithmetic Circuits Aurora[49] 2019 zk-SNARK Yes Yes Yes Arithmetic Circuits zk-STARK[50] 2019 zk-STARK Yes Yes Yes Assembly Zilch[31] 2021 zk-STARK Yes Yes Yes Object-Oriented See also Arrow information paradox Cryptographic protocol Feige–Fiat–Shamir identification scheme Proof of knowledge Topics in cryptography Witness-indistinguishable proof Zero-knowledge password proof Non-interactive zero-knowledge proof References "What is a zero-knowledge proof and why is it useful?". 16 November 2017. 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"SoK: Research Perspectives and Challenges for Bitcoin and Cryptocurrencies". 2015 IEEE Symposium on Security and Privacy. San Jose, California: 104–121. doi:10.1109/SP.2015.14. ISBN 978-1-4673-6949-7. S2CID 549362. Ben-Sasson, Eli; Chiesa, Alessandro; Garman, Christina; Green, Matthew; Miers, Ian; Tromer, Eran; Virza, Madars (18 May 2014). "Zerocash: Decentralized Anonymous Payments from Bitcoin" (PDF). IEEE. Retrieved 26 January 2016. Orcutt, Mike. "A mind-bending cryptographic trick promises to take blockchains mainstream". MIT Technology Review. Retrieved 2017-12-18. Bünz, B; Bootle, D; Boneh, A (2018). "Bulletproofs: Short Proofs for Confidential Transactions and More". IEEE Symposium on Security and Privacy. San Francisco, California: 315–334. doi:10.1109/SP.2018.00020. ISBN 978-1-5386-4353-2. S2CID 3337741. Retrieved 3 December 2020. Odendaal, Hansie; Sharrock, Cayle; Heerden, SW. "Bulletproofs and Mimblewimble". Tari Labs University. Archived from the original on 29 September 2020. Retrieved 3 December 2020. Andrew, Munro (30 July 2019). "Zcoin cryptocurrency introduces zero knowledge proofs with no trusted set-up". Finder Australia. Archived from the original on 30 July 2019. Retrieved 30 July 2019. Aram, Jivanyan (7 April 2019). "Lelantus: Towards Confidentiality and Anonymity of Blockchain Transactions from Standard Assumptions". Cryptology ePrint Archive (Report 373). Retrieved 14 April 2019. Goldreich, Oded (1985). "A zero-knowledge proof that a two-prime moduli is not a Blum integer". Unpublished Manuscript. Goldreich, Oded; Micali, Silvio; Wigderson, Avi (1991). "Proofs that yield nothing but their validity". Journal of the ACM. 38 (3): 690–728. CiteSeerX 10.1.1.420.1478. doi:10.1145/116825.116852. S2CID 2389804. Russell Impagliazzo, Moti Yung: Direct Minimum-Knowledge Computations. CRYPTO 1987: 40-51 Ben-Or, Michael; Goldreich, Oded; Goldwasser, Shafi; Hastad, Johan; Kilian, Joe; Micali, Silvio; Rogaway, Phillip (1990). "Everything provable is provable in zero-knowledge". In Goldwasser, S. (ed.). Advances in Cryptology—CRYPTO '88. Lecture Notes in Computer Science. Vol. 403. Springer-Verlag. pp. 37–56. Ben-or, M.; Goldwasser, Shafi; Kilian, J.; Wigderson, A. (1988). "Multi prover interactive proofs: How to remove intractability assumptions" (PDF). Proceedings of the 20th ACM Symposium on Theory of Computing: 113–121. Dwork, Cynthia; Naor, Moni; Sahai, Amit (2004). "Concurrent Zero Knowledge". Journal of the ACM. 51 (6): 851–898. CiteSeerX 10.1.1.43.716. doi:10.1145/1039488.1039489. S2CID 52827731. Feige, Uriel; Shamir, Adi (1990). Witness Indistinguishable and Witness Hiding Protocols. Proceedings of the Twenty-Second Annual ACM Symposium on Theory of Computing (STOC). pp. 416–426. CiteSeerX 10.1.1.73.3911. doi:10.1145/100216.100272. ISBN 978-0897913614. S2CID 11146395. Mouris, Dimitris; Tsoutsos, Nektarios Georgios (2021). "Zilch: A Framework for Deploying Transparent Zero-Knowledge Proofs". IEEE Transactions on Information Forensics and Security. 16: 3269–3284. doi:10.1109/TIFS.2021.3074869. ISSN 1556-6021. S2CID 222069813. Parno, B.; Howell, J.; Gentry, C.; Raykova, M. (May 2013). "Pinocchio: Nearly Practical Verifiable Computation". 2013 IEEE Symposium on Security and Privacy: 238–252. doi:10.1109/SP.2013.47. ISBN 978-0-7695-4977-4. S2CID 1155080. Costello, Craig; Fournet, Cedric; Howell, Jon; Kohlweiss, Markulf; Kreuter, Benjamin; Naehrig, Michael; Parno, Bryan; Zahur, Samee (May 2015). "Geppetto: Versatile Verifiable Computation". 2015 IEEE Symposium on Security and Privacy: 253–270. doi:10.1109/SP.2015.23. hdl:20.500.11820/37920e55-65aa-4a42-b678-ef5902a5dd45. ISBN 978-1-4673-6949-7. S2CID 3343426. Ben-Sasson, Eli; Chiesa, Alessandro; Genkin, Daniel; Tromer, Eran; Virza, Madars (2013). "SNARKs for C: Verifying Program Executions Succinctly and in Zero Knowledge". Advances in Cryptology – CRYPTO 2013. Lecture Notes in Computer Science. 8043: 90–108. doi:10.1007/978-3-642-40084-1_6. hdl:1721.1/87953. ISBN 978-3-642-40083-4. Wahby, Riad S.; Setty, Srinath; Ren, Zuocheng; Blumberg, Andrew J.; Walfish, Michael (2015). "Efficient RAM and Control Flow in Verifiable Outsourced Computation". Proceedings 2015 Network and Distributed System Security Symposium. doi:10.14722/ndss.2015.23097. ISBN 978-1-891562-38-9. Eberhardt, Jacob; Tai, Stefan (July 2018). "ZoKrates - Scalable Privacy-Preserving Off-Chain Computations". 2018 IEEE International Conference on Internet of Things (IThings) and IEEE Green Computing and Communications (GreenCom) and IEEE Cyber, Physical and Social Computing (CPSCom) and IEEE Smart Data (SmartData): 1084–1091. doi:10.1109/Cybermatics_2018.2018.00199. ISBN 978-1-5386-7975-3. S2CID 49473237. Kosba, Ahmed; Papamanthou, Charalampos; Shi, Elaine (May 2018). "xJsnark: A Framework for Efficient Verifiable Computation". 2018 IEEE Symposium on Security and Privacy (SP): 944–961. doi:10.1109/SP.2018.00018. ISBN 978-1-5386-4353-2. Zhang, Yupeng; Genkin, Daniel; Katz, Jonathan; Papadopoulos, Dimitrios; Papamanthou, Charalampos (May 2018). "vRAM: Faster Verifiable RAM with Program-Independent Preprocessing". 2018 IEEE Symposium on Security and Privacy (SP): 908–925. doi:10.1109/SP.2018.00013. ISBN 978-1-5386-4353-2. Ben-Sasson, Eli; Chiesa, Alessandro; Tromer, Eran; Virza, Madars (20 August 2014). "Succinct non-interactive zero knowledge for a von Neumann architecture". Proceedings of the 23rd USENIX Conference on Security Symposium. USENIX Association: 781–796. ISBN 9781931971157. Kosba, Ahmed; Papadopoulos, Dimitrios; Papamanthou, Charalampos; Song, Dawn (2020). "MIRAGE: Succinct Arguments for Randomized Algorithms with Applications to Universal zk-SNARKs". Cryptology ePrint Archive. Maller, Mary; Bowe, Sean; Kohlweiss, Markulf; Meiklejohn, Sarah (6 November 2019). "Sonic: Zero-Knowledge SNARKs from Linear-Size Universal and Updatable Structured Reference Strings". Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security. Association for Computing Machinery: 2111–2128. doi:10.1145/3319535.3339817. hdl:20.500.11820/739b94f1-54f0-4ec3-9644-3c95eea1e8f5. S2CID 242772913. Chiesa, Alessandro; Hu, Yuncong; Maller, Mary; Mishra, Pratyush; Vesely, Noah; Ward, Nicholas (2020). "Marlin: Preprocessing zkSNARKs with Universal and Updatable SRS". Advances in Cryptology – EUROCRYPT 2020. Lecture Notes in Computer Science. Springer International Publishing. 12105: 738–768. doi:10.1007/978-3-030-45721-1_26. ISBN 978-3-030-45720-4. S2CID 204772154. Gabizon, Ariel; Williamson, Zachary J.; Ciobotaru, Oana (2019). "PLONK: Permutations over Lagrange-bases for Oecumenical Noninteractive arguments of Knowledge". Cryptology ePrint Archive. Bünz, Benedikt; Fisch, Ben; Szepieniec, Alan (2020). "Transparent SNARKs from DARK Compilers". Advances in Cryptology – EUROCRYPT 2020. Lecture Notes in Computer Science. Springer International Publishing. 12105: 677–706. doi:10.1007/978-3-030-45721-1_24. ISBN 978-3-030-45720-4. S2CID 204892714. Wahby, Riad S.; Tzialla, Ioanna; Shelat, Abhi; Thaler, Justin; Walfish, Michael (May 2018). "Doubly-Efficient zkSNARKs Without Trusted Setup". 2018 IEEE Symposium on Security and Privacy (SP): 926–943. doi:10.1109/SP.2018.00060. ISBN 978-1-5386-4353-2. Bowe, Sean; Grigg, Jack; Hopwood, Daira (2019). "Recursive Proof Composition without a Trusted Setup". Cryptology ePrint Archive. Zhang, Jiaheng; Xie, Tiancheng; Zhang, Yupeng; Song, Dawn (May 2020). "Transparent Polynomial Delegation and Its Applications to Zero Knowledge Proof". 2020 IEEE Symposium on Security and Privacy (SP): 859–876. doi:10.1109/SP40000.2020.00052. ISBN 978-1-7281-3497-0. Ames, Scott; Hazay, Carmit; Ishai, Yuval; Venkitasubramaniam, Muthuramakrishnan (30 October 2017). "Ligero: Lightweight Sublinear Arguments Without a Trusted Setup". Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security. Association for Computing Machinery: 2087–2104. doi:10.1145/3133956.3134104. ISBN 9781450349468. S2CID 5348527. Ben-Sasson, Eli; Chiesa, Alessandro; Riabzev, Michael; Spooner, Nicholas; Virza, Madars; Ward, Nicholas P. (2019). "Aurora: Transparent Succinct Arguments for R1CS". Advances in Cryptology – EUROCRYPT 2019. Lecture Notes in Computer Science. Springer International Publishing. 11476: 103–128. doi:10.1007/978-3-030-17653-2_4. ISBN 978-3-030-17652-5. S2CID 52832327. Ben-Sasson, Eli; Bentov, Iddo; Horesh, Yinon; Riabzev, Michael (2019). "Scalable Zero Knowledge with No Trusted Setup". Advances in Cryptology – CRYPTO 2019. Lecture Notes in Computer Science. Springer International Publishing. 11694: 701–732. doi:10.1007/978-3-030-26954-8_23. ISBN 978-3-030-26953-1. S2CID 199501907. Categories: Theory of cryptographyZero-knowledge protocols https://en.wikipedia.org/wiki/Zero-knowledge_proof https://en.wikipedia.org/wiki/List_of_knowledge_deities Category:Zero-knowledge protocols Category Talk Read Edit View history Tools Help From Wikipedia, the free encyclopedia The main article for this category is Zero-knowledge protocol. Pages in category "Zero-knowledge protocols" The following 6 pages are in this category, out of 6 total. This list may not reflect recent changes. A Anonymous veto network C Commitment scheme D Dining cryptographers problem F Feige–Fiat–Shamir identification scheme O Open vote network Z Zero-knowledge proof Categories: Asymmetric-key algorithmsCryptographic protocols https://en.wikipedia.org/wiki/Category:Zero-knowledge_protocols https://en.wikipedia.org/wiki/Law_of_Demeter https://en.wikipedia.org/wiki/Slack_(software) https://en.wikipedia.org/wiki/Uncommon_Knowledge https://en.wikipedia.org/wiki/Threshold_knowledge https://en.wikipedia.org/wiki/Timeline_of_knowledge_about_galaxies,_clusters_of_galaxies,_and_large-scale_structure https://en.wikipedia.org/wiki/Innatism https://en.wikipedia.org/wiki/Rationalism#The_innate_knowledge_thesis https://en.wikipedia.org/wiki/House_of_Knowledge https://en.wikipedia.org/wiki/Knowledge_Quarter https://en.wikipedia.org/wiki/Consilience_(book) https://en.wikipedia.org/wiki/Socrates#Virtue_and_knowledge https://en.wikipedia.org/wiki/Relativism https://en.wikipedia.org/wiki/Vidya_(philosophy) https://en.wikipedia.org/wiki/Knowledge_production_modes https://en.wikipedia.org/wiki/Local_knowledge_problem https://en.wikipedia.org/wiki/The_Postmodern_Condition https://en.wikipedia.org/wiki/Knowledge_translation https://en.wikipedia.org/wiki/Braiding_Sweetgrass https://en.wikipedia.org/wiki/Democratization_of_knowledge https://en.wikipedia.org/wiki/Knowledge_gap_hypothesis https://en.wikipedia.org/wiki/Certainty https://en.wikipedia.org/wiki/STOCK_Act https://en.wikipedia.org/wiki/Knowledge_Is_King https://en.wikipedia.org/wiki/Semantic_Scholar https://en.wikipedia.org/wiki/Knowledge_broker https://en.wikipedia.org/wiki/Route_knowledge https://en.wikipedia.org/wiki/Knowledge-based_processor https://en.wikipedia.org/wiki/Forbidden_knowledge https://en.wikipedia.org/wiki/Wikidata https://en.wikipedia.org/wiki/Encyclopedic_knowledge https://en.wikipedia.org/wiki/Knowledge_space https://en.wikipedia.org/wiki/Knowledge_level https://en.wikipedia.org/wiki/The_Sword_of_Knowledge https://en.wikipedia.org/wiki/Schema_(psychology) https://en.wikipedia.org/wiki/Pedagogy https://en.wikipedia.org/wiki/Experiential_knowledge https://en.wikipedia.org/wiki/Postmodernism https://en.wikipedia.org/wiki/Core_Knowledge https://en.wikipedia.org/wiki/Prop%C3%A6dia#Outline_of_Knowledge https://en.wikipedia.org/wiki/Karl_Popper https://en.wikipedia.org/wiki/Michel_Foucault https://en.wikipedia.org/wiki/Access_to_Knowledge_movement https://en.wikipedia.org/wiki/Hutter_Prize https://en.wikipedia.org/wiki/SECI_model_of_knowledge_dimensions https://en.wikipedia.org/wiki/Consilience_(book) https://en.wikipedia.org/wiki/Everyman_(15th-century_play) https://en.wikipedia.org/wiki/Abhij%C3%B1%C4%81 https://en.wikipedia.org/wiki/Ismail_al-Jazari https://en.wikipedia.org/wiki/Traditional_ecological_knowledge https://en.wikipedia.org/wiki/Pseudoscience https://en.wikipedia.org/wiki/Empiricism https://en.wikipedia.org/wiki/Scientist https://en.wikipedia.org/wiki/An_Essay_on_Criticism https://en.wikipedia.org/wiki/Ornithology#Early_knowledge_and_study https://en.wikipedia.org/wiki/Technological_pedagogical_content_knowledge https://en.wikipedia.org/wiki/Knowledge_Generation_Bureau https://en.wikipedia.org/wiki/University https://en.wikipedia.org/wiki/Knowledge_compilation https://en.wikipedia.org/wiki/Sherlock_Holmes#Knowledge_and_skills https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction https://en.wikipedia.org/wiki/Tree_of_Knowledge_(Australia) https://en.wikipedia.org/wiki/Vocabulary#Productive_and_receptive_knowledge https://en.wikipedia.org/wiki/Appropriation_of_knowledge https://en.wikipedia.org/wiki/Skepticism https://en.wikipedia.org/wiki/Bioprospecting https://en.wikipedia.org/wiki/Frame_(artificial_intelligence)#Frame_language https://en.wikipedia.org/wiki/Mathematical_knowledge_management https://en.wikipedia.org/wiki/Texas_Assessment_of_Knowledge_and_Skills https://en.wikipedia.org/wiki/Augustine_of_Hippo#Natural_knowledge_and_biblical_interpretation https://en.wikipedia.org/wiki/W._Edwards_Deming#The_Deming_System_of_Profound_Knowledge https://en.wikipedia.org/wiki/Follow-the-sun https://en.wikipedia.org/wiki/Non-interactive_zero-knowledge_proof https://en.wikipedia.org/wiki/Terry_Scott_Taylor#Knowledge_&_Innocence https://en.wikipedia.org/wiki/Omniscience https://en.wikipedia.org/wiki/Invention_of_Knowledge https://en.wikipedia.org/wiki/Theaetetus_(dialogue)#Protagoras%27_theory_of_knowledge https://en.wikipedia.org/wiki/Knowledge_neglect https://en.wikipedia.org/wiki/Scientia_sacra https://en.wikipedia.org/wiki/Knowledge_and_Decisions https://en.wikipedia.org/wiki/Proof_of_knowledge https://en.wikipedia.org/wiki/Factual_relativism https://en.wikipedia.org/wiki/Knowledge_Query_and_Manipulation_Language https://en.wikipedia.org/wiki/Knowledge-based_engineering https://en.wikipedia.org/wiki/Multi-factor_authentication https://en.wikipedia.org/wiki/Knowledge_survey https://en.wikipedia.org/wiki/Intellectual_capital https://en.wikipedia.org/wiki/Transcendentalism#Transcendental_knowledge https://en.wikipedia.org/wiki/Theory_of_knowledge_(disambiguation) https://en.wikipedia.org/wiki/A_Culture_of_Conspiracy https://en.wikipedia.org/wiki/A_Treatise_Concerning_the_Principles_of_Human_Knowledge https://en.wikipedia.org/wiki/Objectivity_(philosophy) https://en.wikipedia.org/wiki/Knowledge_regime https://en.wikipedia.org/wiki/The_Social_Construction_of_Reality https://en.wikipedia.org/wiki/Francis_Bacon#Organization_of_knowledge https://en.wikipedia.org/wiki/Knowledge-based_recommender_system https://en.wikipedia.org/wiki/Traditional_medicine#Knowledge_transmission_and_creation https://en.wikipedia.org/wiki/Information_silo https://en.wikipedia.org/wiki/World_Bank#Global_Operations_Knowledge_Management_Unit https://en.wikipedia.org/wiki/Philosophical_skepticism https://en.wikipedia.org/wiki/The_Knowledge:_How_to_Rebuild_Our_World_from_Scratch https://en.wikipedia.org/wiki/Bayes%27_theorem?wprov=srpw1_412 https://en.wikipedia.org/wiki/Mathematician https://en.wikipedia.org/wiki/Zoology https://en.wikipedia.org/wiki/Adam_and_Eve https://en.wikipedia.org/wiki/Foundations_of_the_Science_of_Knowledge https://en.wikipedia.org/wiki/Unity_of_science https://en.wikipedia.org/wiki/Nihilism https://en.wikipedia.org/wiki/Tabula_rasa Meaning of knowledge Linguistic According to the Oxford English Dictionary, the word knowledge refers to "Facts, information, and skills acquired through experience or education; the theoretical or practical understanding of a subject." "In this work on the concept of knowledge, Franz Rosenthal collected a number of definitions of 'ilm, organizing them according to what he saw as their essential elements (admitting that the list was ahistorical and did not necessarily conform to categories the medieval Muslim scholars themselves would have used). Among these definitions, we find the following: Knowledge is the process of knowing, and identical with the knower and the known. Knowledge is that through which one knows. Knowledge is that through which the essence is knowing. Knowledge is that through which the knower is knowing. Knowledge is that which necessitates for him in whom it subsists the name of knower. Knowledge is that which necessitates that he in whom it subsists is knowing. Knowledge is that which necessitates that he in whom it resides (mahall) is knowing. Knowledge stands for ( 'ibarah 'an) the object known ( 'al-ma lum). Knowledge is but the concepts known ( 'al-ma ani al-ma luma). Knowledge is the mentally existing object."[1] Islamic meaning Knowledge in the Western world means information about something, divine or corporeal, while In Islamic point of view 'ilm is an all-embracing term covering theory, action and education, it is not confined to the acquisition of knowledge only, but also embraces socio-political and moral aspects.it requires insight, commitment to the goals of Islam and for the believers to act upon their belief.[2] Also it is reported in hadith that "Knowledge is not extensive learning. Rather, it is a light that God casts in the heart of whomever He wills." [3] https://en.wikipedia.org/wiki/Ilm_(Arabic)#Meaning_of_knowledge https://en.wikipedia.org/wiki/Scientific_Knowledge_and_Its_Social_Problems https://en.wikipedia.org/wiki/Citation https://en.wikipedia.org/wiki/Problem_solving https://en.wikipedia.org/wiki/Modern_flat_Earth_beliefs https://en.wikipedia.org/wiki/Generosity#In_knowledge https://en.wikipedia.org/wiki/Amnesia https://en.wikipedia.org/wiki/Spherical_Earth https://en.wikipedia.org/wiki/Library_Genesis https://en.wikipedia.org/wiki/Third_eye https://en.wikipedia.org/wiki/International_Service_for_the_Acquisition_of_Agri-biotech_Applications#Global_Knowledge_Center_on_Crop_Biotechnology https://en.wikipedia.org/wiki/WolframAlpha https://en.wikipedia.org/wiki/Knowledge-based_authentication https://en.wikipedia.org/wiki/Pre-Socratic_philosophy#Knowledge https://en.wikipedia.org/wiki/Reinforcement_learning https://en.wikipedia.org/wiki/Magician_(fantasy) https://en.wikipedia.org/wiki/Physicist https://en.wikipedia.org/wiki/Test_of_Economic_Knowledge https://en.wikipedia.org/wiki/Precognition https://en.wikipedia.org/wiki/Basic_research https://en.wikipedia.org/wiki/Methodology https://en.wikipedia.org/wiki/Experience https://en.wikipedia.org/wiki/Mens_rea https://en.wikipedia.org/wiki/Schaff%E2%80%93Herzog_Encyclopedia_of_Religious_Knowledge https://en.wikipedia.org/wiki/The_Secret_Knowledge https://en.wikipedia.org/wiki/Penny_Cyclopaedia#National_Cyclopedia_of_Useful_Knowledge https://en.wikipedia.org/wiki/Non-monotonic_logic https://en.wikipedia.org/wiki/Sustainable_Development_Goals https://en.wikipedia.org/wiki/Cognitive_psychology https://en.wikipedia.org/wiki/Human_behavior https://en.wikipedia.org/wiki/Coloniality_of_power#Systems_of_knowledge https://en.wikipedia.org/wiki/Printing https://en.wikipedia.org/wiki/The_Way_to_Divine_Knowledge https://en.wikipedia.org/wiki/Waldwissen https://en.wikipedia.org/wiki/Non-disclosure_agreement https://en.wikipedia.org/wiki/Lexicon https://en.wikipedia.org/wiki/Noble_Eightfold_Path https://en.wikipedia.org/wiki/If_a_tree_falls_in_a_forest#Knowledge_of_the_unobserved_world https://en.wikipedia.org/wiki/History_of_science https://en.wikipedia.org/wiki/Hematology https://en.wikipedia.org/wiki/Justification_(epistemology)#Justification_and_knowledge https://en.wikipedia.org/wiki/Discourse https://en.wikipedia.org/wiki/Unity_of_knowledge_and_action https://en.wikipedia.org/wiki/Tartary https://en.wikipedia.org/wiki/Philanthropedia https://en.wikipedia.org/wiki/Visualization_(graphics) https://en.wikipedia.org/wiki/Nightingale_Pledge https://en.wikipedia.org/wiki/Doctor_of_Science https://en.wikipedia.org/wiki/Expert_system https://en.wikipedia.org/wiki/Walker%27s_Hibernian_Magazine https://en.wikipedia.org/wiki/Critical_theory https://en.wikipedia.org/wiki/Scientific_management https://en.wikipedia.org/wiki/Autodidacticism https://en.wikipedia.org/wiki/Occult https://en.wikipedia.org/wiki/FlatWorld https://en.wikipedia.org/wiki/Paradigm_shift https://en.wikipedia.org/wiki/History_of_mathematics https://en.wikipedia.org/wiki/War_for_talent#Knowledge_work https://en.wikipedia.org/wiki/Technocracy https://en.wikipedia.org/wiki/Supernatural https://en.wikipedia.org/wiki/Fall_of_man https://en.wikipedia.org/wiki/Anthroposophy#Spiritual_knowledge_and_freedom https://en.wikipedia.org/wiki/Aladdin_Knowledge_Systems https://en.wikipedia.org/wiki/Streetwise https://en.wikipedia.org/wiki/List_of_musical_instruments https://en.wikipedia.org/wiki/Celestial_Emporium_of_Benevolent_Knowledge https://en.wikipedia.org/wiki/Analytic_philosophy https://en.wikipedia.org/wiki/Maxim_(philosophy)#Personal_knowledge https://en.wikipedia.org/wiki/Second_language#Depth_of_knowledge https://en.wikipedia.org/wiki/Moksha https://en.wikipedia.org/wiki/Mutual_knowledge https://en.wikipedia.org/wiki/Diffusion_of_innovations https://en.wikipedia.org/wiki/Hinterland#Breadth_of_knowledge https://en.wikipedia.org/wiki/Rhetoric#Knowledge https://en.wikipedia.org/wiki/Consistency_(knowledge_bases) https://en.wikipedia.org/wiki/Innocence#In_relation_to_knowledge https://en.wikipedia.org/wiki/World_of_Knowledge https://en.wikipedia.org/wiki/Intelligence_agency https://en.wikipedia.org/wiki/Contamination https://en.wikipedia.org/wiki/Positivism https://en.wikipedia.org/wiki/Hockney%E2%80%93Falco_thesis https://en.wikipedia.org/wiki/Paradise_Lost https://en.wikipedia.org/wiki/Ethics https://en.wikipedia.org/wiki/Engineering https://en.wikipedia.org/wiki/School https://en.wikipedia.org/wiki/Christian_mysticism#False_spiritual_knowledge https://en.wikipedia.org/wiki/Human%E2%80%93computer_interaction#Knowledge-driven_human%E2%80%93computer_interaction https://en.wikipedia.org/wiki/Notice#Notice_and_knowledge https://en.wikipedia.org/wiki/Falsifiability https://en.wikipedia.org/wiki/Fionn_mac_Cumhaill https://en.wikipedia.org/wiki/Outline_of_epistemology https://en.wikipedia.org/wiki/Cognitive_robotics#Knowledge_acquisition https://en.wikipedia.org/wiki/Writing#Scientific_and_scholarly_knowledge_production https://en.wikipedia.org/wiki/Is%E2%80%93ought_problem https://en.wikipedia.org/wiki/The_Degrees_of_Knowledge https://en.wikipedia.org/wiki/Genetic_epistemology#Types_of_knowledge https://en.wikipedia.org/wiki/The_Universal_Magazine_of_Knowledge_and_Pleasure https://en.wikipedia.org/wiki/Divergent_(novel)#Social_structure_and_knowledge https://en.wikipedia.org/wiki/Anti-pattern https://en.wikipedia.org/wiki/Compendium

Category:Phonetic transcription symbols

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• 0–9
• A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Pages in category "Phonetic transcription symbols"

The following 109 pages are in this category, out of 109 total. This list may not reflect recent changes.

A

• Ȧ
• Ă
• Ā
• Ã
• Æ
• Latin alpha

B

• Ɓ
• Ƀ
• Small capital B
• Beta
• Bilabial click

C

• Ç
• Ć
• Ċ
• Č
• Ƈ
• Stretched C
• Ȼ
• C with bar
• Chi (letter)
• Click letter

D

• Ḍ
• African D
• Ɗ
• D with hook and tail
• D with stroke
• Eth
• Db ligature
• Double grave accent

E

• Ẽ
• Ə
• Eng (letter)
• Latin epsilon

G

• Ǧ
• Ġ
• Insular G
• Ɠ
• Glottal stop (letter)
• Gamma
• Latin gamma

ɡ

• ꬶ

H

• Ḫ
• Heng (letter)
• H with stroke
• Turned h with fishhook
• Ḥ

I

• Ɨ
• Ɪ
• Latin iota

J

• J̌

K

• K with diagonal stroke
• Ƙ
• K with stroke
• K with stroke and diagonal stroke

L

• Ł
• Barred lambda
• Latin beta
• Latin turned alpha

M

• Ɱ
• Modifier letter left half ring
• Modifier letter right half ring

N

• Ñ
• N with long right leg
• Ɲ

O

• Ɵ
• Ö
• Ǫ
• Ø
• Œ
• ⱺ
• Open O

P

• P with stroke
• Ƥ
• Palatal hook
• Phonetic Symbol Guide

Q

• Q with stroke
• Qp ligature

R

• Ȓ
• R with tail

S

• S͎
• S with swash tail
• Š
• Ṡ
• S̀
• Esh (letter)

T

• Ƭ
• Ʈ
• Theta
• Tie (typography)
• Turned A
• Turned h

U

• U bar
• Ŭ

V

• V with diagonal stroke
• Ʋ
• Turned v
• V with curl
• Voiced labiodental flap

W

• Ɯ

X

• X̣

Y

• Ý
• Ÿ (vowel)
• Yogh

Z

• Z with swash tail
• Ezh
• Ź
• Ž
• Z̀
• Ǯ

Categories:

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• Phonetic alphabets

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In linguistics, a count noun (also countable noun) is a noun that can be modified by a quantity and that occurs in both singular and plural forms, and that can co-occur with quantificational determiners like every, each, several, etc. A mass noun has none of these properties: It cannot be modified by a number, cannot occur in plural, and cannot co-occur with quantificational determiners. 

https://en.wikipedia.org/wiki/Count_noun

A determiner, also called determinative (abbreviated DET), is a word, phrase, or affix that occurs together with a noun or noun phrase and generally serves to express the reference of that noun or noun phrase in the context. That is, a determiner may indicate whether the noun is referring to a definite or indefinite element of a class, to a closer or more distant element, to an element belonging to a specified person or thing, to a particular number or quantity, etc. Common kinds of determiners include definite and indefinite articles (the, a), demonstratives (this, that), possessive determiners (my, their), cardinal numerals (one, two), quantifiers (many, both), distributive determiners (each, every), and interrogative determiners (which, what). 

For the written element in logographic scripts, see Determinative.

 

https://en.wikipedia.org/wiki/Determiner

 

 

In linguistics, definiteness is a semantic feature of noun phrases, distinguishing between referents or senses that are identifiable in a given context (definite noun phrases) and those which are not (indefinite noun phrases). The prototypical definite noun phrase picks out a unique, familiar, specific referent such as the sun or Australia, as opposed to indefinite examples like an idea or some fish.

There is considerable variation in the expression of definiteness across languages, and some languages such as Japanese do not generally mark it so that the same expression could be definite in some contexts and indefinite in others. In other languages, such as English, it is usually marked by the selection of determiner (e.g., the vs a). In still other languages, such as Danish, definiteness is marked morphologically. 

https://en.wikipedia.org/wiki/Definiteness

 

 

Iron meteorites, also called siderites or ferrous meteorites, are a type of meteorite that consist overwhelmingly of an iron–nickel alloy known as meteoric iron that usually consists of two mineral phases: kamacite and taenite. Most iron meteorites originate from cores of planetesimals,^[2] with the exception of the IIE iron meteorite group^[3]

The iron found in iron meteorites was one of the earliest sources of usable iron available to humans, due to the malleability and ductility of the meteoric iron,^[4] before the development of smelting that signaled the beginning of the Iron Age. 

Iron meteorite
— Type —
Tamentit Iron Meteorite, found in 1864 in the Sahara,[1] weighing about 500 kg (1,100 lb). On display at Vulcania park in France.

https://en.wikipedia.org/wiki/Iron_meteorite

Count-classifiers and mass-classifiers

A classifier categorizes a class of nouns by picking out some salient perceptual properties...which are permanently associated with entities named by the class of nouns; a measure word does not categorize but denotes the quantity of the entity named by a noun.

— Tai (1994, p. 2), emphasis added

Within the set of nominal classifiers, linguists generally draw a distinction between "count-classifiers" and "mass-classifiers". True count-classifiers^{[note 8]} are used for naming or counting a single count noun,^[15] and have no direct translation in English; for example, 一本书 (yì běn shū, one-CL book) can only be translated in English as "one book" or "a book".^[20] Furthermore, count-classifiers cannot be used with mass nouns: just as an English speaker cannot ordinarily say *"five muds", a Chinese speaker cannot say *五个泥 (wǔ ge nì, five-CL mud). For such mass nouns, one must use mass-classifiers.^{[15][note 9]}

Mass-classifiers (true measure words) do not pick out inherent properties of an individual noun like count-classifiers do; rather, they lump nouns into countable units. Thus, mass-classifiers can generally be used with multiple types of nouns; for example, while the mass-classifier 盒 (hé, box) can be used to count boxes of lightbulbs (一盒灯泡 yì hé dēngpào, "one box of lightbulbs") or of books (一盒教材 yì hé jiàocái, "one box of textbooks"), each of these nouns must use a different count-classifier when being counted by itself (一盏灯泡 yì zhǎn dēngpào "one lightbulb"; vs. 一本教材 yì běn jiàocái "one textbook"). While count-classifiers have no direct English translation, mass-classifiers often do: phrases with count-classifiers such as 一个人 (yí ge rén, one-CL person) can only be translated as "one person" or "a person", whereas those with mass-classifiers such as 一群人 (yì qún rén, one-crowd-person) can be translated as "a crowd of people". All languages, including English, have mass-classifiers, but count-classifiers are unique to certain "classifier languages", and are not a part of English grammar apart from a few exceptional cases such as head of livestock.^[21]

Within the range of mass-classifiers, authors have proposed subdivisions based on the manner in which a mass-classifier organizes the noun into countable units. One of these is measurement units (also called "standard measures"),^[22] which all languages must have in order to measure items; this category includes units such as kilometers, liters, or pounds^[23] (see list). Like other classifiers, these can also stand without a noun; thus, for example, 磅 (bàng, pound) may appear as both 三磅肉 (sān bàng ròu, "three pounds of meat") or just 三磅 (sān bàng, "three pounds", never *三个磅 sān ge bàng).^[24] Units of currency behave similarly: for example, 十元 (shí yuán, "ten yuan"), which is short for (for example) 十元人民币 (shí yuán rénmínbì, "ten units of renminbi"). Other proposed types of mass-classifiers include "collective"^{[25][note 10]} mass-classifiers, such as 一群人 (yì qún rén, "a crowd of people"), which group things less precisely; and "container"^[26] mass-classifiers which group things by containers they come in, as in 一碗粥 (yì wǎn zhōu, "a bowl of porridge") or 一包糖 (yì bāo táng, "a bag of sugar").

The difference between count-classifiers and mass-classifiers can be described as one of quantifying versus categorizing: in other words, mass-classifiers create a unit by which to measure something (i.e. boxes, groups, chunks, pieces, etc.), whereas count-classifiers simply name an existing item.^[27] Most words can appear with both count-classifiers and mass-classifiers; for example, pizza can be described as both 一张比萨 (yì zhāng bǐsà, "one pizza", literally "one pie of pizza"), using a count-classifier, and as 一块比萨 (yí kuài bǐsà, "one piece of pizza"), using a mass-classifier. In addition to these semantic differences, there are differences in the grammatical behaviors of count-classifiers and mass-classifiers;^[28] for example, mass-classifiers may be modified by a small set of adjectives (as in 一大群人 yí dà qún rén, "a big crowd of people"), whereas count-classifiers usually may not (for example, *一大个人 yí dà ge rén is never said for "a big person"; instead the adjective must modify the noun: 一个大人 yí ge dà rén).^[29] Another difference is that count-classifiers may often be replaced by a "general" classifier 个 (個), gè with no apparent change in meaning, whereas mass-classifiers may not.^[30] Syntacticians Lisa Cheng and Rint Sybesma propose that count-classifiers and mass-classifiers have different underlying syntactic structures, with count-classifiers forming "classifier phrases",^{[note 11]} and mass-classifiers being a sort of relative clause that only looks like a classifier phrase.^[31] The distinction between count-classifiers and mass-classifiers is often unclear, however, and other linguists have suggested that count-classifiers and mass-classifiers may not be fundamentally different. They posit that "count-classifier" and "mass-classifier" are the extremes of a continuum, with most classifiers falling somewhere in between.^[32]

Verbal classifiers

There is a set of "verbal classifiers" used specifically for counting the number of times an action occurs, rather than counting a number of items; this set includes 次 cì, 遍/徧 biàn, 回 huí, and 下 xià, which all roughly translate to "times".^[33] For example, 我去过三次北京 (wǒ qù-guo sān cì Běijīng, I go-PAST three-CL Beijing, "I have been to Beijing three times").^[34] These words can also form compound classifiers with certain nouns, as in 人次 rén cì "person-time", which can be used to count (for example) visitors to a museum in a year (where visits by the same person on different occasions are counted separately).

Another type of verbal classifier indicates the tool or implement used to perform the action. An example is found in the sentence 他踢了我一脚 tā tī le wǒ yī jiǎo "he kicked me", or more literally "he kicked me one foot". The word 脚 jiǎo, which usually serves as a simple noun meaning "foot", here functions as a verbal classifier reflecting the tool (namely the foot) used to perform the kicking action.

Relation to nouns

鱼 yú
"fish"

裤子 kùzi
"(pair of) pants"

河 hé
"river"

凳子 dèngzi
"long bench"

The above nouns denoting long or flexible objects may all appear with the classifier 条 (條) tiáo in certain dialects such as Mandarin.^[35] In Mandarin, 一条板凳 means "a CL bench", and if people want to say "a chair", 個/个 or 張/张 is used because 条 is only used for referring to relatively long things. In other dialects such as Cantonese, 條 cannot be used to refer to 櫈. Instead, 張 is used.

Different classifiers often correspond to different particular nouns. For example, books generally take the classifier 本 běn, flat objects take 张 (張) zhāng, animals take 只 (隻) zhī, machines take 台 tái, large buildings and mountains take 座 zuò, etc. Within these categories are further subdivisions—while most animals take 只 (隻) zhī, domestic animals take 头 (頭) tóu, long and flexible animals take 条 (條) tiáo, and horses take 匹 pǐ. Likewise, while long things that are flexible (such as ropes) often take 条 (條) tiáo, long things that are rigid (such as sticks) take 根 gēn, unless they are also round (like pens or cigarettes), in which case in some dialects they take 枝 zhī.^[36] Classifiers also vary in how specific they are; some (such as 朵 duǒ for flowers and other similarly clustered items) are generally only used with one type, whereas others (such as 条 (條) tiáo for long and flexible things, one-dimensional things, or abstract items like news reports)^{[note 12]} are much less restricted.^[37] Furthermore, there is not a one-to-one relationship between nouns and classifiers: the same noun may be paired with different classifiers in different situations.^[38] The specific factors that govern which classifiers are paired with which nouns have been a subject of debate among linguists.

Categories and prototypes

While mass-classifiers do not necessarily bear any semantic relationship to the noun with which they are used (e.g. box and book are not related in meaning, but one can still say "a box of books"), count-classifiers do.^[31] The precise nature of that relationship, however, is not certain, since there is so much variability in how objects may be organized and categorized by classifiers. Accounts of the semantic relationship may be grouped loosely into categorical theories, which propose that count-classifiers are matched to objects solely on the basis of inherent features of those objects (such as length or size), and prototypical theories, which propose that people learn to match a count-classifier to a specific prototypical object and to other objects that are like that prototype.^[39]

The categorical, "classical"^[40] view of classifiers was that each classifier represents a category with a set of conditions; for example, the classifier 条 (條) tiáo would represent a category defined as all objects that meet the conditions of being long, thin, and one-dimensional—and nouns using that classifier must fit all the conditions with which the category is associated. Some common semantic categories into which count-classifiers have been claimed to organize nouns include the categories of shape (long, flat, or round), size (large or small), consistency (soft or hard), animacy (human, animal, or object),^[41] and function (tools, vehicles, machines, etc.).^[42]

A mule
骡子, luózi

A donkey
驴子, lǘzi

James Tai and Wang Lianqing found that the horse classifier 匹 pǐ is sometimes used for mules and camels, but rarely for the less "horse-like" donkeys, suggesting that the choice of classifiers is influenced by prototypal closeness.^[43]

On the other hand, proponents of prototype theory propose that count-classifiers may not have innate definitions, but are associated with a noun that is prototypical of that category, and nouns that have a "family resemblance" with the prototype noun will want to use the same classifier.^{[note 13]} For example, horse in Chinese uses the classifier 匹 pǐ, as in 三匹马 (sān pǐ mǎ, "three horses")—in modern Chinese the word 匹 has no meaning. Nevertheless, nouns denoting animals that look like horses will often also use this same classifier, and native speakers have been found to be more likely to use the classifier 匹 the closer an animal looks to a horse.^[43] Furthermore, words that do not meet the "criteria" of a semantic category may still use that category because of their association with a prototype. For example, the classifier 颗 (顆) kē is used for small round items, as in 一颗子弹 (yì kē zǐdàn, "one bullet"); when words like 原子弹 (yuánzǐdàn, "atomic bomb") were later introduced into the language they also used this classifier, even though they are not small and round—therefore, their classifier must have been assigned because of the words' association with the word for bullet, which acted as a "prototype".^[44] This is an example of "generalization" from prototypes: Erbaugh has proposed that when children learn count-classifiers, they go through stages, first learning a classifier-noun pair only (such as 条鱼 tiáo yú, CL-fish), then using that classifier with multiple nouns that are similar to the prototype (such as other types of fish), then finally using that set of nouns to generalize a semantic feature associated with the classifier (such as length and flexibility) so that the classifier can then be used with new words that the person encounters.^[45]

Some classifier-noun pairings are arbitrary, or at least appear to modern speakers to have no semantic motivation.^[46] For instance, the classifier 部 bù may be used for movies and novels, but also for cars^[47] and telephones.^[48] Some of this arbitrariness may be due to what linguist James Tai refers to as "fossilization", whereby a count-classifier loses its meaning through historical changes but remains paired with some nouns. For example, the classifier 匹 pǐ used for horses is meaningless today, but in Classical Chinese may have referred to a "team of two horses",^[49] a pair of horse skeletons,^[50] or the pairing between man and horse.^{[51][note 14]} Arbitrariness may also arise when a classifier is borrowed, along with its noun, from a dialect in which it has a clear meaning to one in which it does not.^[52] In both these cases, the use of the classifier is remembered more by association with certain "prototypical" nouns (such as horse) rather than by understanding of semantic categories, and thus arbitrariness has been used as an argument in favor of the prototype theory of classifiers.^[52] Gao and Malt propose that both the category and prototype theories are correct: in their conception, some classifiers constitute "well-defined categories", others make "prototype categories", and still others are relatively arbitrary.^[53]

Neutralization

In addition to the numerous "specific" count-classifiers described above,^{[note 15]} Chinese has a "general" classifier 个 (個), pronounced gè in Mandarin.^{[note 16]} This classifier is used for people, some abstract concepts, and other words that do not have special classifiers (such as 汉堡包 hànbǎobāo "hamburger"),^[54] and may also be used as a replacement for a specific classifier such as 张 (張) zhāng or 条 (條) tiáo, especially in informal speech. In Mandarin Chinese, it has been noted as early as the 1940s that the use of 个 is increasing and that there is a general tendency towards replacing specific classifiers with it.^[55] Numerous studies have reported that both adults and children tend to use 个 when they do not know the appropriate count-classifier, and even when they do but are speaking quickly or informally.^[56] The replacement of a specific classifier with the general 个 is known as classifier neutralization^[57] ("量词个化" in Chinese, literally "classifier 个-ization"^[58]). This occurs especially often among children^[59] and aphasics (individuals with damage to language-relevant areas of the brain),^[60][61] although normal speakers also neutralize frequently. It has been reported that most speakers know the appropriate classifiers for the words they are using and believe, when asked, that those classifiers are obligatory, but nevertheless use 个 without even realizing it in actual speech.^[62] As a result, in everyday spoken Mandarin the general classifier is "hundreds of times more frequent"^[63] than the specialized ones.

Nevertheless, 个 has not completely replaced other count-classifiers, and there are still many situations in which it would be inappropriate to substitute it for the required specific classifier.^[55] There may be specific patterns behind which classifier-noun pairs may be "neutralized" to use the general classifier, and which may not. Specifically, words that are most prototypical for their categories, such as paper for the category of nouns taking the "flat/square" classifier 张 (張) zhāng, may be less likely to be said with a general classifier.^[64]

Variation in usage

A painting may be referred to with the classifiers 张 (張) zhāng and 幅 fú; both phrases have the same meaning, but convey different stylistic effects.^[65]

Depending on the classifier used, the noun 楼 lóu could be used to refer to either this building, as in 一座楼 (yí zuò lóu "one building"), or the floors of the building, as in 二十层楼 (èrshí céng lóu, "twenty floors").^[66]

It is not the case that every noun is only associated with one classifier. Across dialects and speakers there is great variability in the way classifiers are used for the same words, and speakers often do not agree which classifier is best.^[67] For example, for cars some people use 部 bù, others use 台 tái, and still others use 辆 (輛) liàng; Cantonese uses 架 gaa3. Even within a single dialect or a single speaker, the same noun may take different measure words depending on the style in which the person is speaking, or on different nuances the person wants to convey (for instance, measure words can reflect the speaker's judgment of or opinion about the object^[68]). An example of this is the word for person, 人 rén, which uses the measure word 个 (個) gè normally, but uses the measure 口 kǒu when counting number of people in a household, 位 wèi when being particularly polite or honorific, and 名 míng in formal, written contexts;^[69] likewise, a group of people may be referred to by massifiers as 一群人 (yì qún rén, "a group of people") or 一帮人 (yì bāng rén, "a gang/crowd of people"): the first is neutral, whereas the second implies that the people are unruly or otherwise being judged poorly.^[70]

Some count-classifiers may also be used with nouns that they are not normally related to, for metaphorical effect, as in 一堆烦恼 (yì duī fánnǎo, "a pile of worries/troubles").^[71] Finally, a single word may have multiple count-classifiers that convey different meanings altogether—in fact, the choice of a classifier can even influence the meaning of a noun. By way of illustration, 三节课 sān jié kè means "three class periods" (as in "I have three classes today"), whereas 三门课 sān mén kè means "three courses" (as in "I signed up for three courses this semester"), even though the noun in each sentence is the same.^[66]

Purpose

In research on classifier systems, and Chinese classifiers in particular, it has been asked why count-classifiers (as opposed to mass-classifiers) exist at all. Mass-classifiers are present in all languages since they are the only way to "count" mass nouns that are not naturally divided into units (as, for example, "three splotches of mud" in English; *"three muds" is ungrammatical). On the other hand, count-classifiers are not inherently mandatory, and are absent from most languages.^{[21][note 17]} Furthermore, count-classifiers are used with an "unexpectedly low frequency";^[72] in many settings, speakers avoid specific classifiers by just using a bare noun (without a number or demonstrative) or using the general classifier 个 gè.^[73] Linguists and typologists such as Joseph Greenberg have suggested that specific count-classifiers are semantically "redundant", repeating information present within the noun.^[74] Count-classifiers can be used stylistically, though,^[69] and can also be used to clarify or limit a speaker's intended meaning when using a vague or ambiguous noun; for example, the noun 课 kè "class" can refer to courses in a semester or specific class periods during a day, depending on whether the classifier 门 (門) mén or 节 (節) jié is used.^[75]

One proposed explanation for the existence of count-classifiers is that they serve more of a cognitive purpose than a practical one: in other words, they provide a linguistic way for speakers to organize or categorize real objects.^[76] An alternative account is that they serve more of a discursive and pragmatic function (a communicative function when people interact) rather than an abstract function within the mind.^[73] Specifically, it has been proposed that count-classifiers might be used to mark new or unfamiliar objects within a discourse,^[76] to introduce major characters or items in a story or conversation,^[77] or to foreground important information and objects by making them bigger and more salient.^[78] In this way, count-classifiers might not serve an abstract grammatical or cognitive function, but may help in communication by making important information more noticeable and drawing attention to it.

History

Classifier phrases

An oracle bone inscription from the Shāng Dynasty. Such inscriptions provide some of the earliest examples of the number phrases that may have eventually spawned Chinese classifiers.

Historical linguists have found that phrases consisting of nouns and numbers went through several structural changes in Old Chinese and Middle Chinese before classifiers appeared in them. The earliest forms may have been Number – Noun, like English (i.e. "five horses"), and the less common Noun – Number ("horses five"), both of which are attested in the oracle bone scripts of Pre-Archaic Chinese (circa 1400 BCE to 1000 BCE).^[79] The first constructions resembling classifier constructions were Noun – Number – Noun constructions, which were also extant in Pre-Archaic Chinese but less common than Number – Noun. In these constructions, sometimes the first and second nouns were identical (N1 – Number – N1, as in "horses five horses") and other times the second noun was different, but semantically related (N1 – Number – N2). According to some historical linguists, the N2 in these constructions can be considered an early form of count-classifier and has even been called an "echo classifier"; this speculation is not universally agreed on, though.^[80] Although true count-classifiers had not appeared yet, mass-classifiers were common in this time, with constructions such as "wine – six – yǒu" (the word 酉 yǒu represented a wine container) meaning "six yǒu of wine".^[80] Examples such as this suggest that mass-classifiers predate count-classifiers by several centuries, although they did not appear in the same word order as they do today.^[81]

It is from this type of structure that count-classifiers may have arisen, originally replacing the second noun (in structures where there was a noun rather than a mass-classifier) to yield Noun – Number – Classifier. That is to say, constructions like "horses five horses" may have been replaced by ones like "horses five CL", possibly for stylistic reasons such as avoiding repetition.^[82] Another reason for the appearance of count-classifiers may have been to avoid confusion or ambiguity that could have arisen from counting items using only mass-classifiers—i.e. to clarify when one is referring to a single item and when one is referring to a measure of items.^[83]

Historians agree that at some point in history the order of words in this construction shifted, putting the noun at the end rather than beginning, like in the present-day construction Number – Classifier – Noun.^[84] According to historical linguist Alain Peyraube, the earliest occurrences of this construction (albeit with mass-classifiers, rather than count-classifiers) appear in the late portion of Old Chinese (500 BCE to 200 BCE). At this time, the Number – Mass-classifier portion of the Noun – Number – Mass-classifier construction was sometimes shifted in front of the noun. Peyraube speculates that this may have occurred because it was gradually reanalyzed as a modifier (like an adjective) for the head noun, as opposed to a simple repetition as it originally was. Since Chinese generally places modifiers before modified, as does English, the shift may have been prompted by this reanalysis. By the early part of the Common Era, the nouns appearing in "classifier position" were beginning to lose their meaning and become true classifiers. Estimates of when classifiers underwent the most development vary: Wang Li claims their period of major development was during the Han Dynasty (206 BCE – 220 CE),^[85] whereas Liu Shiru estimates that it was the Southern and Northern Dynasties period (420 – 589 CE),^[86] and Peyraube chooses the Tang Dynasty (618 – 907 CE).^[87] Regardless of when they developed, Wang Lianqing claims that they did not become grammatically mandatory until sometime around the 11th century.^[88]

Classifier systems in many nearby languages and language groups (such as Vietnamese and the Tai languages) are very similar to the Chinese classifier system in both grammatical structure and the parameters along which some objects are grouped together. Thus, there has been some debate over which language family first developed classifiers and which ones then borrowed them—or whether classifier systems were native to all these languages and developed more through repeated language contact throughout history.^[89]

Classifier words

Most modern count-classifiers are derived from words that originally were free-standing nouns in older varieties of Chinese, and have since been grammaticalized to become bound morphemes.^[90] In other words, count-classifiers tend to come from words that once had specific meaning but lost it (a process known as semantic bleaching).^[91] Many, however, still have related forms that work as nouns all by themselves, such as the classifier 带 (帶) dài for long, ribbon-like objects: the modern word 带子 dàizi means "ribbon".^[71] In fact, the majority of classifiers can also be used as other parts of speech, such as nouns.^[92] Mass-classifiers, on the other hand, are more transparent in meaning than count-classifiers; while the latter have some historical meaning, the former are still full-fledged nouns. For example, 杯 (bēi, cup), is both a classifier as in 一杯茶 (yì bēi chá, "a cup of tea") and the word for a cup as in 酒杯 (jiǔbēi, "wine glass").^[93]

Where do these classifiers come from? Each classifier has its own history.

— Peyraube (1991, p. 116)

It was not always the case that every noun required a count-classifier. In many historical varieties of Chinese, use of classifiers was not mandatory, and classifiers are rare in writings that have survived.^[94] Some nouns acquired classifiers earlier than others; some of the first documented uses of classifiers were for inventorying items, both in mercantile business and in storytelling.^[95] Thus, the first nouns to have count-classifiers paired with them may have been nouns that represent "culturally valued" items such as horses, scrolls, and intellectuals.^[96] The special status of such items is still apparent today: many of the classifiers that can only be paired with one or two nouns, such as 匹 pǐ for horses^{[note 18]} and 首 shǒu for songs or poems, are the classifiers for these same "valued" items. Such classifiers make up as much as one-third of the commonly used classifiers today.^[19]

Classifiers did not gain official recognition as a lexical category (part of speech) until the 20th century. The earliest modern text to discuss classifiers and their use was Ma Jianzhong's 1898 Ma's Basic Principles for Writing Clearly (马氏文通).^[97] From then until the 1940s, linguists such as Ma, Wang Li, and Li Jinxi treated classifiers as just a type of noun that "expresses a quantity".^[85] Lü Shuxiang was the first to treat them as a separate category, calling them "unit words" (单位词 dānwèicí) in his 1940s Outline of Chinese Grammar (中国文法要略) and finally "measure words" (量词 liàngcí) in Grammar Studies (语法学习). He made this separation based on the fact that classifiers were semantically bleached, and that they can be used directly with a number, whereas true nouns need to have a measure word added before they can be used with a number.^[98] After this time, other names were also proposed for classifiers: Gao Mingkai called them "noun helper words" (助名词 zhùmíngcí), Lu Wangdao "counting markers" (计标 jìbiāo), and Japanese linguist Miyawaki Kennosuke called them "accompanying words" (陪伴词 péibàncí).^[99] In the Draft Plan for a System of Teaching Chinese Grammar [zh] adopted by the People's Republic of China in 1954, Lü's "measure words" (量词 liàngcí) was adopted as the official name for classifiers in China.^[100] This remains the most common term in use today.^[12]

General classifiers

Historically, 个 gè was not always the general classifier. Some believe it was originally a noun referring to bamboo stalks, and gradually expanded in use to become a classifier for many things with "vertical, individual, [or] upright qualit[ies]",^[101] eventually becoming a general classifier because it was used so frequently with common nouns.^[102] The classifier gè is actually associated with three different homophonous characters: 个, 個 (used today as the traditional-character equivalent of 个), and 箇. Historical linguist Lianqing Wang has argued that these characters actually originated from different words, and that only 箇 had the original meaning of "bamboo stalk".^[103] 个, he claims, was used as a general classifier early on, and may have been derived from the orthographically similar 介 jiè, one of the earliest general classifiers.^[104] 箇 later merged with 介 because they were similar in pronunciation and meaning (both used as general classifiers).^[103] Likewise, he claims that 個 was also a separate word (with a meaning having to do with "partiality" or "being a single part"), and merged with 个 for the same reasons as 箇 did; he also argues that 個 was "created", as early as the Han Dynasty, to supersede 个.^[105]

Nor was 个 the only general classifier in the history of Chinese. The aforementioned 介 jiè was being used as a general classifier before the Qin Dynasty (221 BCE); it was originally a noun referring to individual items out of a string of connected shells or clothes, and eventually came to be used as a classifier for "individual" objects (as opposed to pairs or groups of objects) before becoming a general classifier.^[106] Another general classifier was 枚 méi, which originally referred to small twigs. Since twigs were used for counting items, 枚 became a counter word: any items, including people, could be counted as "one 枚, two 枚", etc. 枚 was the most common classifier in use during the Southern and Northern Dynasties period (420–589 CE),^[107] but today is no longer a general classifier, and is only used rarely, as a specialized classifier for items such as pins and badges.^[108] Kathleen Ahrens has claimed that 隻 (zhī in Mandarin and jia in Taiwanese), the classifier for animals in Mandarin, is another general classifier in Taiwanese and may be becoming one in the Mandarin spoken in Taiwan.^[109]

Variety

Northern dialects tend to have fewer classifiers than southern ones. 個 ge is the only classifier found in the Dungan language. All nouns could have just one classifier in some dialects, such as Shanghainese (Wu), the Mandarin dialect of Shanxi, and Shandong dialects. Some dialects such as Northern Min, certain Xiang dialects, Hakka dialects, and some Yue dialects use 隻 for the noun referring to people, rather than 個.^[110]

See also

• China portal
• Languages portal

• List of Chinese classifiers
• Chinese grammar
• Collective noun
• Classifiers in other languages:
  • Burmese numerical classifiers
  • Hokkien counter word
  • Japanese counter word
  • Korean counter word
  • Vietnamese classifier

Notes

1. 
   

All examples given in this article are from standard Mandarin Chinese, with pronunciation indicated using the pinyin system, unless otherwise stated. The script would often be identical in other varieties of Chinese, although the pronunciation would vary.

Across different varieties of Chinese, classifier-noun clauses have slightly different interpretations (particularly in the interpretation of definiteness in classified nouns as opposed to bare nouns), but the requirement that a classifier come between a number and a noun is more or less the same in the major varieties (Cheng & Sybesma 2005).

Although “每” (每个人) is more generally used to mean "every person" in this case.

See, for example, similar results in the Chinese corpus of the Center for Chinese Linguistics at Peking University: 天空一片, retrieved on 3 June 2009.

In addition to the count-mass distinction and nominal-verbal distinction described below, various linguists have proposed many additional divisions of classifiers by type. He (2001, chapters 2 and 3) contains a review of these.

The Syllabus of Graded Words and Characters for Chinese Proficiency is a standardized measure of vocabulary and character recognition, used in the People's Republic of China for testing middle school students, high school students, and foreign learners. The most recent edition was published in 2003 by the Testing Center of the National Chinese Proficiency Testing Committee.

Including the following:

• Chen, Baocun 陈保存 (1988). Chinese Classifier Dictionary 汉语量词词典. Fuzhou: Fujian People's Publishing House 福建人民出版社. ISBN 978-7-211-00375-4.
• Fang, Jiqing; Connelly; Michael (2008). Chinese Measure Word Dictionary. Boston: Cheng & Tsui. ISBN 978-0-88727-632-3.
• Jiao, Fan 焦凡 (2001). A Chinese-English Dictionary of Measure Words 汉英量词词典. Beijing: Sinolingua 华语敎学出版社. ISBN 978-7-80052-568-1.
• Liu, Ziping 刘子平 (1996). Chinese Classifier Dictionary 汉语量词词典. Inner Mongolia Education Press 内蒙古教育出版社. ISBN 978-7-5311-2707-9.

Count-classifiers have also been called "individual classifiers", (Chao 1968, p. 509), "qualifying classifiers" (Zhang 2007, p. 45; Hu 1993, p. 10), and just "classifiers" (Cheng & Sybesma 1998, p. 3).

Mass-classifiers have also been called "measure words", "massifiers" (Cheng & Sybesma 1998, p. 3), "non-individual classifiers" (Chao 1968, p. 509), and "quantifying classifiers" (Zhang 2007, p. 45; Hu 1993, p. 10). The term "mass-classifier" is used in this article to avoid ambiguous usage of the term "measure word", which is often used in everyday speech to refer to both count-classifiers and mass-classifiers, even though in technical usage it only means mass-classifiers (Li 2000, p. 1116).

Also called "aggregate" (Li & Thompson 1981, pp. 107–109) or "group" (Ahrens 1994, p. 239, note 3) measures.

"Classifier phrases" are similar to noun phrases, but with a classifier rather than a noun as the head (Cheng & Sybesma 1998, pp. 16–17).

This may be because official documents during the Han Dynasty were written on long bamboo strips, making them "strips of business" (Ahrens 1994, p. 206).

The theory described in Ahrens (1994) and Wang (1994) is also referred to within those works as a "prototype" theory, but differs somewhat from the version of prototype theory described here; rather than claiming that individual prototypes are the source for classifier meanings, these authors believe that classifiers still are based on categories with features, but that the categories have many features, and "prototypes" are words that have all the features of that category whereas other words in the category only have some features. In other words, "there are core and marginal members of a category.... a member of a category does not necessarily possess all the properties of that category" (Wang 1994, p. 8). For instance, the classifier 棵 kē is used for the category of trees, which may have features such as "has a trunk", "has leaves", and "has branches", "is deciduous"; maple trees would be prototypes of the category, since they have all these features, whereas palm trees only have a trunk and leaves and thus are not prototypical (Ahrens 1994, pp. 211–12).

The apparent disagreement between the definitions provided by different authors may reflect different uses of these words in different time periods. It is well-attested that many classifiers underwent frequent changes of meaning throughout history (Wang 1994; Erbaugh 1986, pp. 426–31; Ahrens 1994, pp. 205–206), so 匹 pǐ may have had all these meanings at different points in history.

Also called "sortal classifiers" (Erbaugh 2000, p. 33; Biq 2002, p. 531).

Kathleen Ahrens claimed in 1994 that the classifier for animals—只 (隻), pronounced zhī in Mandarin and jia in Taiwanese—is in the process of becoming a second general classifier in the Mandarin spoken in Taiwan, and already is used as the general classifier in Taiwanese itself (Ahrens 1994, p. 206).

Although English does not have a productive system of count-classifiers and is not considered a "classifier language", it does have a few constructions—mostly archaic or specialized—that resemble count-classifiers, such as "X head of cattle" (T'sou 1976, p. 1221).

18. Today, 匹 may also be used for bolts of cloth. See "List of Common Nominal Measure Words" on ChineseNotes.com (last modified 11 January 2009; retrieved on 3 September 2009).

References

1. 
   

Li & Thompson 1981, p. 104

Hu 1993, p. 13

The examples are adapted from those given in Hu (1993, p. 13), Erbaugh (1986, pp. 403–404), and Li & Thompson (1981, pp. 104–105).

Zhang 2007, p. 47

Li 2000, p. 1119

Sun 2006, p. 159

Sun 2006, p. 160

Li & Thompson 1981, p. 82

Li & Thompson 1981, pp. 34–35

Li & Thompson 1981, p. 111

Hu 1993, p. 9

Li 2000, p. 1116; Hu 1993, p. 7; Wang 1994, pp. 22, 24–25; He 2001, p. 8. Also see the usage in Fang & Connelly (2008) and most introductory Chinese textbooks.

Li & Thompson 1981, p. 105

Chao 1968, section 7.9

Zhang 2007, p. 44

Erbaugh 1986, p. 403; Fang & Connelly 2008, p. ix

He 2001, p. 234

Gao & Malt 2009, p. 1133

Erbaugh 1986, p. 403

Erbaugh 1986, p. 404

Tai 1994, p. 3; Allan 1977, pp. 285–86; Wang 1994, p. 1

Ahrens 1994, p. 239, note 3

Li & Thompson 1981, p. 105; Zhang 2007, p. 44; Erbaugh 1986, p. 118, note 5

Li & Thompson 1981, pp. 105–107

Erbaugh 1986, p. 118, note 5; Hu 1993, p. 9

Erbaugh 1986, p. 118, note 5; Li & Thompson 1981, pp. 107–109

Cheng & Sybesma 1998, p. 3; Tai 1994, p. 2

Wang 1994, pp. 27–36; Cheng & Sybesma 1998

Cheng & Sybesma 1998, pp. 3–5

Wang 1994, pp. 29–30

Cheng & Sybesma 1998

Ahrens 1994, p. 239, note 5; Wang 1994, pp. 26–27, 37–48

He 2001, pp. 42, 44

Zhang 2007, p. 44; Li & Thompson 1981, p. 110; Fang & Connelly 2008, p. x

Tai 1994, p. 8

Tai 1994, pp. 7–9; Tai & Wang 1990

Erbaugh 1986, p. 111

He 2001, p. 239

Tai 1994, pp. 3–5; Ahrens 1994, pp. 208–12

Tai 1994, p. 3; Ahrens 1994, pp. 209–10

Tai 1994, p. 5; Allan 1977

Hu 1993, p. 1

Tai 1994, p. 12

Zhang 2007, pp. 46–47

Erbaugh 1986, p. 415

Hu 1993, p. 1; Tai 1994, p. 13; Zhang 2007, pp. 55–56

Zhang 2007, pp. 55–56

Gao & Malt 2009, p. 1134

Morev 2000, p. 79

Wang 1994, pp. 172–73

Tai 1994, p. 15, note 7

Tai 1994, p. 13

Gao & Malt 2009, pp. 1133–4

Hu 1993, p. 12

Tzeng, Chen & Hung 1991, p. 193

Zhang 2007, p. 57

Ahrens 1994, p. 212

He 2001, p. 165

Erbaugh 1986; Hu 1993

Ahrens 1994, pp. 227–32

Tzeng, Chen & Hung 1991

Erbaugh 1986, pp. 404–406; Ahrens 1994, pp. 202–203

Erbaugh 1986, pp. 404–406

Ahrens 1994

Zhang 2007, p. 53

Zhang 2007, p. 52

Tai 1994; Erbaugh 2000, pp. 34–35

He 2001, p. 237

Fang & Connelly 2008, p. ix; Zhang 2007, pp. 53–54

He 2001, p. 242

Shie 2003, p. 76

Erbaugh 2000, p. 34

Erbaugh 2000, pp. 425–26; Li 2000

Zhang 2007, p. 51

Zhang 2007, pp. 51–52

Erbaugh 1986, pp. 425–6

Sun 1988, p. 298

Li 2000

Peyraube 1991, p. 107; Morev 2000, pp. 78–79

Peyraube 1991, p. 108

Peyraube 1991, p. 110; Wang 1994, pp. 171–72

Morev 2000, pp. 78–79

Wang 1994, p. 172

Peyraube 1991, p. 106; Morev 2000, pp. 78–79

He 2001, p. 3

Wang 1994, pp. 2, 17

Peyraube 1991, pp. 111–17

Wang 1994, p. 3

Erbaugh 1986, p. 401; Wang 1994, p. 2

Shie 2003, p. 76; Wang 1994, pp. 113–14, 172–73

Peyraube 1991, p. 116

Gao & Malt 2009, p. 1130

Chien, Lust & Chiang 2003, p. 92

Peyraube 1991; Erbaugh 1986, p. 401

Erbaugh 1986, p. 401

Erbaugh 1986, pp. 401, 403, 428

He 2001, p. 2

He 2001, p. 4

He 2001, pp. 5–6

He 2001, p. 7

Erbaugh 1986, p. 430

Erbaugh 1986, pp. 428–30; Ahrens 1994, p. 205

Wang 1994, pp. 114–15

Wang 1994, p. 95

Wang 1994, pp. 115–16, 158

Wang 1994, pp. 93–95

Wang 1994, pp. 155–7

Erbaugh 1986, p. 428

Ahrens 1994, p. 206

110. Graham Thurgood; Randy J. LaPolla (2003). Graham Thurgood, Randy J. LaPolla (ed.). The Sino-Tibetan languages. Routledge language family. Vol. 3 (illustrated ed.). Psychology Press. p. 85. ISBN 0-7007-1129-5. Retrieved 2012-03-10. In general, the Southern dialects have a greater number of classifiers than the Northern. The farther north one travels, the smaller the variety of classifiers found. In Dunganese, a Gansu dialect of Northern Chinese spoken in Central Asia, only one classifier, 個 [kə], is used; and this same classifier has almost become the cover classifier for all nouns in Lánzhou of Gansu too. The tendency to use one general classifier for all nouns is also found to a greater or lesser extent in many Shanxi dialects, some Shandong dialects, and even the Shanghai dialect of Wu and Standard Mandarin (SM). The choice of classifiers for individual nouns is particular to each dialect. For example, although the preferred classifier across dialects for 'human being' is 個 and its cognates, 隻 in its dialect forms is widely used in the Hakka and Yue dialects of Guangxi and western Guangdong provinces as well as in the Northern Min dialects and some Xiang dialects in Hunan.

Bibliography

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• Allan, Keith (1977). "Classifiers". Language. Linguistic Society of America. 53 (2): 285–311. doi:10.2307/413103. JSTOR 413103.
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• Chao, Yuen Ren (1968). A Grammar of Spoken Chinese. Berkeley: University of California Press.
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• Cheng, Lisa L.-S.; Sybesma, Rint (2005). "Classifiers in four varieties of Chinese". In Cinque, Guglielmo; Kayne, Richard S. (eds.). The Oxford Handbook of Comparative Syntax. Oxford University Press. ISBN 0-19-513650-0.
• Chien, Yu-Chin; Lust, Barbara; Chiang, Chi-Pang (2003). "Chinese children's comprehension of count-classifiers and mass-classifiers". Journal of East Asian Linguistics. 12 (2): 91–120. doi:10.1023/A:1022401006521.
• Erbaugh, Mary S. (1986). "Taking stock: the development of Chinese noun classifiers historically and in young children". In Colette Craig (ed.). Noun classes and categorization. J. Benjamins. pp. 399–436. ISBN 978-0-915027-33-0.
• Erbaugh, Mary S. (2000). Classifiers are for specification: complementary functions for sortal and general classifiers in Cantonese and Mandarin. 33rd International Conference on Sino-Tibetan Languages and Linguistics.
• Fang, Jiqing; Connelly, Michael (2008). Chinese Measure Word Dictionary. Boston: Cheng & Tsui. ISBN 978-0-88727-632-3.
• Gao, Ming; Malt, Barbara (2009). "Mental representation and cognitive consequences of Chinese individual classifiers". Language and Cognitive Processes. 24 (7/8): 1124–1179. doi:10.1080/01690960802018323.
• He, Jie (何杰) (2001). Studies on classifiers in Modern Chinese (现代汉语量词研究) (in Chinese) (2nd ed.). Beijing: Nationalities Publishing House (民族出版社). ISBN 978-7-105-04714-7.
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• Li, Charles N.; Thompson, Sandra A. (1981). Mandarin Chinese: A Functional Reference Grammar. Los Angeles: University of California Press. ISBN 978-0-520-06610-6.
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External links

• List of Common Nominal Measure Words on chinesenotes.com
• Units of Weights and Measures on chinesenotes.com
• How to Use Chinese Measure Words on 3000 Hanzi

v t e Chinese language or Sinitic languages

Categories:

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Single-crystalline GeTe nanowires and nanohelices

Semiconducting GeTe nanowires (NW) and nanohelices (NH) are synthesized via vapor transport method, with metal nanoparticle catalysts. GeTe was evaporated and carried by Ar gas at optimum temperature, pressure, time, and gas flow rate to the downstream collecting/grow site (SiO₂ surface coated with colloidal gold nanoparticles). High temperature over 500 °C produces thicker nanowires and crystalline chunks. Au is essential to the growth of NW and NH and is suggested to the metal catalyst of the reaction. This method gives rise to NW and NH with a 1:1 ratio of Ge and Te. NW produced by this method average about 65 nm in diameter and up to 50 μm in length. NHs averages to 135 nm in helix diameter.^[9]

Nanocrystal (quantum size effect)

The synthesis described above has not reached the sized required to exhibit quantum size effect. Nanostructures that reach the quantum regime exhibit a different set of phenomena unseen at a larger scale, for example, spontaneous polar ordering and the splitting of diffraction spots. The synthesis of GeTe nanocrystals of average size of 8, 17, and 100 nm involves divalent Ge(II) chloride – 1,4 dioxane complex and bis[bis(trimethylsilyl)amino]Ge (II) and trioctylphosphine-tellurium in a solvent such as 1,2-dichlorobenzene or phenyl ether. Ge(II) reduction kinetics has been thought to determine the GeTe formation. Large the Ge(II) reduction rate may lead to the increase in particle nucleation rate, resulting in the reduction of particle diameter.^[10] 

https://en.wikipedia.org/wiki/Germanium_telluride#Single-crystalline_GeTe_nanowires_and_nanohelices

 

"Hymn to the Fallen" (Jiu Ge) (traditional Chinese: 國殤; simplified Chinese: 国殇; pinyin: Guó shāng; lit. 'National casualties') is a Classical Chinese poem which has been preserved in the Nine Songs (Jiu Ge) section of the ancient Chinese poetry anthology, the Chu ci, or The Songs of Chu, which is an ancient set of poems. Together, these poems constitute one of the 17 sections of the poetry anthology which was published under the title of the Chuci (also known as the Songs of Chu or as the Songs of the South). Despite the "Nine" in the title (Jiu ge literally means Nine Songs), the number of these poetic pieces actually consists of eleven separate songs, or elegies.^[1] This set of verses seems to represent some shamanistic dramatic practices of the Yangzi River valley area (as well as a northern tradition or traditions) involving the invocation of divine beings and seeking their blessings by means of a process of courtship.^[2] The poetry consists of lyrics written for performance as part of a religious drama, however the lack of stage directions or indications of who is supposed to be singing at any one time or whether some of the lines represent lines for a chorus makes an accurate reconstruction of how such a shamanic drama would actually have been performed quite uncertain; although, there are internal textual clues, for example indicating the use of spectacular costumes for the performers, and an extensive orchestra.^[3] Although not precisely dated, "Hymn to the Fallen" dates from the end of the late the Warring States period, ended 221 BCE, with possible revisions in the Han dynasty, particularly during the reign of Han Wudi, during 141 to 87 BCE . The poem has been translated into English by David Hawkes as "Hymn to the Fallen". "Guo shang" is a hymn to soldiers killed in war. Guó (國) means the "state", "kingdom", or "nation". Shāng (殤) means to "die young". Put together, the title refers to those who meet death in the course of fighting for their country. David Hawkes describes it as "surely one of the most beautiful laments for fallen soldiers in any language".^[4] 

https://en.wikipedia.org/wiki/Hymn_to_the_Fallen_(Jiu_Ge)

 

 

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In computer architecture, registers are typically addressed by mechanisms other than main memory, but may in some cases be assigned a memory address e.g. DEC PDP-10, ICT 1900.[2] Almost all computers, whether load/store architecture or not, load items of data from a larger memory into registers where they are used for arithmetic operations, bitwise operations, and other operations, and are manipulated or tested by machine instructions. Manipulated items are then often stored back to main memory, either by the same instruction or by a subsequent one. Modern processors use either static or dynamic RAM as main memory, with the latter usually accessed via one or more cache levels. Processor registers are normally at the top of the memory hierarchy, and provide the fastest way to access data. The term normally refers only to the group of registers that are directly encoded as part of an instruction, as defined by the instruction set. However, modern high-performance CPUs often have duplicates of these "architectural registers" in order to improve performance via register renaming, allowing parallel and speculative execution. Modern x86 design acquired these techniques around 1995 with the releases of Pentium Pro, Cyrix 6x86, Nx586, and AMD K5. When a computer program accesses the same data repeatedly, this is called locality of reference. Holding frequently used values in registers can be critical to a program's performance. Register allocation is performed either by a compiler in the code generation phase, or manually by an assembly language programmer. https://en.wikipedia.org/wiki/Processor_register Size Registers are normally measured by the number of bits they can hold, for example, an "8-bit register", "32-bit register", "64-bit register", or even more. In some instruction sets, the registers can operate in various modes, breaking down their storage memory into smaller parts (32-bit into four 8-bit ones, for instance) to which multiple data (vector, or one-dimensional array of data) can be loaded and operated upon at the same time. Typically it is implemented by adding extra registers that map their memory into a larger register. Processors that have the ability to execute single instructions on multiple data are called vector processors. https://en.wikipedia.org/wiki/Processor_register A geolocation-based video game or location-based video game is a type of video game where the gameplay evolves and progresses via a player's location in the world, often attained using GPS. Most location-based video games are mobile games that make use of the mobile phone's built in GPS capability, and often have real-world map integration. One of the most recognizable location-based mobile games is Pokémon Go. Location-based (GPS) games are often conflated with augmented reality (AR) games. GPS and AR are two separate technologies which are sometimes both used in a game, like in Pokémon Go and Minecraft Earth. GPS and AR functionality largely do not depend on one another but are often used in concert. A video game may be an AR game, a location-based game, both, or neither. https://en.wikipedia.org/wiki/Geolocation-based_video_game https://en.wikipedia.org/wiki/Augmented_reality https://en.wikipedia.org/wiki/Alternate_reality https://en.wikipedia.org/wiki/Multiverse https://en.wikipedia.org/wiki/Virtual_reality https://en.wikipedia.org/wiki/Simulation_hypothesis https://en.wikipedia.org/wiki/Realization_(probability) https://en.wikipedia.org/wiki/Empirical_probability Realization is the art of creating music, typically an accompaniment, from a figured bass, whether by improvisation in real time, or as a detained exercise in writing. It is most commonly associated with Baroque music. https://en.wikipedia.org/wiki/Realization_(figured_bass) Realization, also called Biographie, is a circa 35-metre (115 ft) sport climbing route on a limestone cliff on the southern face of Céüse mountain, near Gap and Sigoyer, in France. After it was first climbed in 2001 by American climber Chris Sharma, it became the first rock climb in the world to have a consensus grade of 9a+ (5.15a).[a] It is considered an historic and important route in rock climbing, and one of the most attempted climbs at its grade.[5][6] https://en.wikipedia.org/wiki/Realization_(climb) In metrology, the realisation of a unit of measure is the conversion of its definition into reality.[1] The International vocabulary of metrology identifies three distinct methods of realisation: Realisation of a measurement unit from its definition. Reproduction of measurement standards. Adopting a particular artefact as a standard. The International Bureau of Weights and Measures maintains the techniques for realisation of the base units in the International System of Units (SI).[2] https://en.wikipedia.org/wiki/Realisation_(metrology) Realized niche width is a phrase relating to ecology, is defined by the actual space that an organism inhabits and the resources it can access as a result of limiting pressures from other species (e.g. superior competitors). An organism's ecological niche is determined by the biotic and abiotic factors that make up that specific ecosystem that allow that specific organism to survive there. The width of an organism's niche is set by the range of conditions a species is able to survive in that specific environment. https://en.wikipedia.org/wiki/Realized_niche_width Realizing Increased Photosynthetic Efficiency (RIPE) is a translational research project that is genetically engineering plants to photosynthesize more efficiently to increase crop yields.[1] RIPE aims to increase agricultural production worldwide, particularly to help reduce hunger and poverty in Sub-Saharan Africa and Southeast Asia by sustainably improving the yield of key food crops including soybeans, rice, cassava[2] and cowpeas.[3] The RIPE project began in 2012, funded by a five-year, $25-million dollar grant from the Bill and Melinda Gates Foundation.[4] In 2017, the project received a $45 million-dollar reinvestment from the Gates Foundation, Foundation for Food and Agriculture Research, and the UK Government's Department for International Development.[5] In 2018, the Gates Foundation contributed an additional $13 million to accelerate the project's progress.[6] https://en.wikipedia.org/wiki/Realizing_Increased_Photosynthetic_Efficiency Realized variance or realised variance (RV, see spelling differences) is the sum of squared returns. For instance the RV can be the sum of squared daily returns for a particular month, which would yield a measure of price variation over this month. More commonly, the realized variance is computed as the sum of squared intraday returns for a particular day. The realized variance is useful because it provides a relatively accurate measure of volatility[1] which is useful for many purposes, including volatility forecasting and forecast evaluation. https://en.wikipedia.org/wiki/Realized_variance The Age of Enlightenment or the Enlightenment,[note 2] also known as the Age of Reason, was an intellectual and philosophical movement that occurred in Europe in the 17th and 18th centuries, with global influences and effects.[2][3] The Enlightenment included a range of ideas centered on the value of human happiness, the pursuit of knowledge obtained by means of reason and the evidence of the senses, and ideals such as natural law, liberty, progress, toleration, fraternity, constitutional government, and separation of church and state.[4][5] https://en.wikipedia.org/wiki/Age_of_Enlightenment https://en.wikipedia.org/wiki/Knowledge Definitions of knowledge try to determine the essential features of knowledge. Closely related terms are conception of knowledge, theory of knowledge, and analysis of knowledge. Some general features of knowledge are widely accepted among philosophers, for example, that it constitutes a cognitive success or an epistemic contact with reality and that propositional knowledge involves true belief. Most definitions of knowledge in analytic philosophy focus on propositional knowledge or knowledge-that, as in knowing that Dave is at home, in contrast to knowledge-how (know-how) expressing practical competence. However, despite the intense study of knowledge in epistemology, the disagreements about its precise nature are still both numerous and deep. Some of those disagreements arise from the fact that different theorists have different goals in mind: some try to provide a practically useful definition by delineating its most salient feature or features, while others aim at a theoretically precise definition of its necessary and sufficient conditions. Further disputes are caused by methodological differences: some theorists start from abstract and general intuitions or hypotheses, others from concrete and specific cases, and still others from linguistic usage. Additional disagreements arise concerning the standards of knowledge: whether knowledge is something rare that demands very high standards, like infallibility, or whether it is something common that requires only the possession of some evidence. One definition that many philosophers consider to be standard, and that has been discussed since ancient Greek philosophy, is justified true belief (JTB). This implies that knowledge is a mental state and that it is not possible to know something false. There is widespread agreement among analytic philosophers that knowledge is a form of true belief. The idea that justification is an additionally required component is due to the intuition that true beliefs based on superstition, lucky guesses, or erroneous reasoning do not constitute knowledge. In this regard, knowledge is more than just being right about something. The source of most disagreements regarding the nature of knowledge concerns what more is needed. According to the standard philosophical definition, it is justification. The original account understands justification internalistically as another mental state of the person, like a perceptual experience, a memory, or a second belief. This additional mental state supports the known proposition and constitutes a reason or evidence for it. However, some modern versions of the standard philosophical definition use an externalistic conception of justification instead. Many such views affirm that a belief is justified if it was produced in the right way, for example, by a reliable cognitive process. The justified-true-belief definition of knowledge came under severe criticism in the second half of the 20th century, mainly due to a series of counterexamples given by Edmund Gettier. Most of these examples aim to illustrate cases in which a justified true belief does not amount to knowledge because its justification is not relevant to its truth. This is often termed epistemic luck since it is just a fortuitous coincidence that the justified belief is also true. A few epistemologists have concluded from these counterexamples that the JTB definition of knowledge is deeply flawed and have sought a radical reconception of knowledge. However, many theorists still agree that the JTB definition is on the right track and have proposed more moderate responses to deal with the suggested counterexamples. Some hold that modifying one's conception of justification is sufficient to avoid them. Another approach is to include an additional requirement besides justification. On this view, being a justified true belief is a necessary but not a sufficient condition of knowledge. A great variety of such criteria has been suggested. They usually manage to avoid many of the known counterexamples but they often fall prey to newly proposed cases. It has been argued that, in order to circumvent all Gettier cases, the additional criterion needs to exclude epistemic luck altogether. However, this may require the stipulation of a very high standard of knowledge: that nothing less than infallibility is needed to exclude all forms of luck. The defeasibility theory of knowledge is one example of a definition based on a fourth criterion besides justified true belief. The additional requirement is that there is no truth that would constitute a defeating reason of the belief if the person knew about it. Other alternatives to the JTB definition are reliabilism, which holds that knowledge has to be produced by reliable processes, causal theories, which require that the known fact caused the knowledge, and virtue theories, which identify knowledge with the manifestation of intellectual virtues. Not all forms of knowledge are propositional, and various definitions of different forms of non-propositional knowledge have also been proposed. But among analytic philosophers this field of inquiry is less active and characterized by less controversy. Someone has practical knowledge or know-how if they possess the corresponding competence or ability. Knowledge by acquaintance constitutes a relation not to a proposition but to an object. It is defined as familiarity with its object based on direct perceptual experience of it. https://en.wikipedia.org/wiki/Definitions_of_knowledge Knowledge transfer is the sharing or disseminating of knowledge and the providing of inputs to problem solving.[1] In organizational theory, knowledge transfer is the practical problem of transferring knowledge from one part of the organization to another. Like knowledge management, knowledge transfer seeks to organize, create, capture or distribute knowledge and ensure its availability for future users. It is considered to be more than just a communication problem. If it were merely that, then a memorandum, an e-mail or a meeting would accomplish the knowledge transfer. Knowledge transfer is more complex because: knowledge resides in organizational members, tools, tasks, and their subnetworks[2] and much knowledge in organizations is tacit or hard to articulate.[3] The subject has been taken up under the title of knowledge management since the 1990s. The term has also been applied to the transfer of knowledge at the international level.[4][5] In business, knowledge transfer now has become a common topic in mergers and acquisitions.[6] It focuses on transferring technological platform, market experience, managerial expertise, corporate culture, and other intellectual capital that can improve the companies' competence.[7] Since technical skills and knowledge are very important assets for firms' competence in the global competition,[8] unsuccessful knowledge transfer can have a negative impact on corporations and lead to the expensive and time-consuming M&A not creating values to the firms.[9] https://en.wikipedia.org/wiki/Knowledge_transfer Knowledge extraction is the creation of knowledge from structured (relational databases, XML) and unstructured (text, documents, images) sources. The resulting knowledge needs to be in a machine-readable and machine-interpretable format and must represent knowledge in a manner that facilitates inferencing. Although it is methodically similar to information extraction (NLP) and ETL (data warehouse), the main criterion is that the extraction result goes beyond the creation of structured information or the transformation into a relational schema. It requires either the reuse of existing formal knowledge (reusing identifiers or ontologies) or the generation of a schema based on the source data. The RDB2RDF W3C group [1] is currently standardizing a language for extraction of resource description frameworks (RDF) from relational databases. Another popular example for knowledge extraction is the transformation of Wikipedia into structured data and also the mapping to existing knowledge (see DBpedia and Freebase). https://en.wikipedia.org/wiki/Knowledge_extraction In philosophy, a distinction is often made between two different kinds of knowledge: knowledge by acquaintance and knowledge by description. Whereas knowledge by description is something like ordinary propositional knowledge (e.g. "I know that snow is white"), knowledge by acquaintance is familiarity with a person, place, or thing, typically obtained through perceptual experience (e.g. "I know Sam", "I know the city of Bogotá", or "I know Russell's Problems of Philosophy").[1] According to Bertrand Russell's classic account of acquaintance knowledge, acquaintance is a direct causal interaction between a person and some object that the person is perceiving. https://en.wikipedia.org/wiki/Knowledge_by_acquaintance The knowledge economy (or the knowledge-based economy) is an economic system in which the production of goods and services is based principally on knowledge-intensive activities that contribute to advancement in technical and scientific innovation.[1] The key element of value is the greater dependence on human capital and intellectual property for the source of the innovative ideas, information and practices.[2] Organisations are required to capitalise this "knowledge" into their production to stimulate and deepen the business development process. There is less reliance on physical input and natural resources. A knowledge-based economy relies on the crucial role of intangible assets within the organisations' settings in facilitating modern economic growth.[3] https://en.wikipedia.org/wiki/Knowledge_economy The knowledge argument (also known as Mary's Room or Mary the super-scientist) is a philosophical thought experiment proposed by Frank Jackson in his article "Epiphenomenal Qualia" (1982) and extended in "What Mary Didn't Know" (1986). The experiment describes Mary, a scientist who exists in a black-and-white world where she has extensive access to physical descriptions of color, but no actual perceptual experience of color. Mary has learned everything there is to learn about color, but she has never actually experienced it for herself. The central question of the thought experiment is whether Mary will gain new knowledge when she goes outside the colorless world and experiences seeing in color https://en.wikipedia.org/wiki/Knowledge_argument Knowledge management (KM) is the collection of methods relating to creating, sharing, using and managing the knowledge and information of an organization.[1] It refers to a multidisciplinary approach to achieve organizational objectives by making the best use of knowledge.[2] https://en.wikipedia.org/wiki/Knowledge_management Embedding of a knowledge graph. The vector representation of the entities and relations can be used for different machine learning applications. In representation learning, knowledge graph embedding (KGE), also referred to as knowledge representation learning (KRL), or multi-relation learning,[1] is a machine learning task of learning a low-dimensional representation of a knowledge graph's entities and relations while preserving their semantic meaning.[1][2][3] Leveraging their embedded representation, knowledge graphs (KGs) can be used for various applications such as link prediction, triple classification, entity recognition, clustering, and relation extraction.[1][4] https://en.wikipedia.org/wiki/Knowledge_graph_embedding A relationship extraction task requires the detection and classification of semantic relationship mentions within a set of artifacts, typically from text or XML documents. The task is very similar to that of information extraction (IE), but IE additionally requires the removal of repeated relations (disambiguation) and generally refers to the extraction of many different relationships. https://en.wikipedia.org/wiki/Relationship_extraction A document is a written, drawn, presented, or memorialized representation of thought, often the manifestation of non-fictional, as well as fictional, content. The word originates from the Latin Documentum, which denotes a "teaching" or "lesson": the verb doceō denotes "to teach". In the past, the word was usually used to denote written proof useful as evidence of a truth or fact. In the Computer Age, "document" usually denotes a primarily textual computer file, including its structure and format, e.g. fonts, colors, and images. Contemporarily, "document" is not defined by its transmission medium, e.g., paper, given the existence of electronic documents. "Documentation" is distinct because it has more denotations than "document". Documents are also distinguished from "realia", which are three-dimensional objects that would otherwise satisfy the definition of "document" because they memorialize or represent thought; documents are considered more as 2-dimensional representations. While documents can have large varieties of customization, all documents can be shared freely and have the right to do so, creativity can be represented by documents, also. History, events, examples, opinions, etc. all can be expressed in documents. https://en.wikipedia.org/wiki/Document In library classification systems, realia are three-dimensional objects from real life such as coins, tools, and textiles, that do not fit into the traditional categories of library material. They can be either man-made (artifacts, tools, utensils, etc.) or naturally occurring (specimens, samples, etc.), usually borrowed, purchased, or received as donation by a teacher, library, or museum for use in classroom instruction or in exhibits. Archival and manuscript collections often receive items of memorabilia such as badges, emblems, insignias, jewelry, leather goods, needlework, etc., in connection with gifts of personal papers. Most government or institutional archives reject gifts of non-documentary objects unless they have a documentary value. When accepting large bequests of mixed objects they normally have the donors sign legal documents giving permission to the archive to destroy, exchange, sell, or dispose in any way those objects which, according to the best judgement of the archivist, are not manuscripts (which can include typescripts or printouts) or are not immediately useful for understanding the manuscripts. Recently, the usage of this term has been criticized by librarians based on the usage of term realia to refer to artistic and historical artifacts and objects, and suggesting the use of the phrase "real world object" to describe the broader categories of three-dimensional objects in libraries. https://en.wikipedia.org/wiki/Realia_(library_science) https://en.wikipedia.org/wiki/Knowledge_Web https://en.wikipedia.org/wiki/Commonsense_knowledge_(artificial_intelligence) https://en.wikipedia.org/wiki/Zero_knowledge https://en.wikipedia.org/wiki/Knowledge_Network https://en.wikipedia.org/wiki/Tacit_knowledge https://en.wikipedia.org/wiki/Procedural_knowledge https://en.wikipedia.org/wiki/The_Archaeology_of_Knowledge https://en.wikipedia.org/wiki/Knowledge_distillation https://en.wikipedia.org/wiki/Definitions_of_knowledge https://en.wikipedia.org/wiki/Knowledge_representation_and_reasoning https://en.wikipedia.org/wiki/Divine_knowledge https://en.wikipedia.org/wiki/Curse_of_knowledge https://en.wikipedia.org/wiki/Decolonization_of_knowledge https://en.wikipedia.org/wiki/Science https://en.wikipedia.org/wiki/Word_of_Knowledge https://en.wikipedia.org/wiki/Knowledge_base https://en.wikipedia.org/wiki/Encyclopedia https://en.wikipedia.org/wiki/Desacralization_of_knowledge https://en.wikipedia.org/wiki/Meta-knowledge https://en.wikipedia.org/wiki/Metacognition#Metastrategic_knowledge https://en.wikipedia.org/wiki/Core_Knowledge_Foundation https://en.wikipedia.org/wiki/Western_esotericism https://en.wikipedia.org/wiki/Dangerous_Knowledge https://en.wikipedia.org/wiki/Coloniality_of_knowledge https://en.wikipedia.org/wiki/Gettier_problem https://en.wikipedia.org/wiki/Artificial_intelligence#Knowledge_representation https://en.wikipedia.org/wiki/Ontology_language#Classification_of_ontology_languages https://en.wikipedia.org/wiki/Academic_discipline https://en.wikipedia.org/wiki/Forbidden_fruit https://en.wikipedia.org/wiki/Knowledge,_Skills,_and_Abilities https://en.wikipedia.org/wiki/Knowledge_Navigator https://en.wikipedia.org/wiki/Knowledge_and_Its_Limits https://en.wikipedia.org/wiki/Monopolies_of_knowledge https://en.wikipedia.org/wiki/Knowledge_(legal_construct) https://en.wikipedia.org/wiki/Empirical_evidence https://en.wikipedia.org/wiki/Self-knowledge https://en.wikipedia.org/wiki/Tree_of_the_knowledge_of_good_and_evil https://en.wikipedia.org/wiki/Knowledge_acquisition https://en.wikipedia.org/wiki/Open_knowledge https://en.wikipedia.org/wiki/Book_of_Knowledge https://en.wikipedia.org/wiki/Taxes_on_knowledge https://en.wikipedia.org/wiki/General_knowledge https://en.wikipedia.org/wiki/Zero-knowledge_proof From Wikipedia, the free encyclopedia "ZKP" redirects here. For the airport in Russia, see Zyryanka Airport. For other uses, see Zero knowledge. In cryptography, a zero-knowledge proof or zero-knowledge protocol is a method by which one party (the prover) can prove to another party (the verifier) that a given statement is true while the prover avoids conveying any additional information apart from the fact that the statement is indeed true. The essence of zero-knowledge proofs is that it is trivial to prove that one possesses knowledge of certain information by simply revealing it; the challenge is to prove such possession without revealing the information itself or any additional information.[1] If proving a statement requires that the prover possess some secret information, then the verifier will not be able to prove the statement to anyone else without possessing the secret information. The statement being proved must include the assertion that the prover has such knowledge, but without including or transmitting the knowledge itself in the assertion. Otherwise, the statement would not be proved in zero-knowledge because it provides the verifier with additional information about the statement by the end of the protocol. A zero-knowledge proof of knowledge is a special case when the statement consists only of the fact that the prover possesses the secret information. Interactive zero-knowledge proofs require interaction between the individual (or computer system) proving their knowledge and the individual validating the proof.[1] This section needs to be updated. The reason given is: There are also Non-interactive zero-knowledge proofs. Please help update this article to reflect recent events or newly available information. (December 2022) A protocol implementing zero-knowledge proofs of knowledge must necessarily require interactive input from the verifier. This interactive input is usually in the form of one or more challenges such that the responses from the prover will convince the verifier if and only if the statement is true, i.e., if the prover does possess the claimed knowledge. If this were not the case, the verifier could record the execution of the protocol and replay it to convince someone else that they possess the secret information. The new party's acceptance is either justified since the replayer does possess the information (which implies that the protocol leaked information, and thus, is not proved in zero-knowledge), or the acceptance is spurious, i.e., was accepted from someone who does not actually possess the information. Some forms of non-interactive zero-knowledge proofs exist,[2][3] but the validity of the proof relies on computational assumptions (typically the assumptions of an ideal cryptographic hash function). Abstract examples The Ali Baba cave Peggy randomly takes either path A or B, while Victor waits outside Victor chooses an exit path Peggy reliably appears at the exit Victor names There is a well-known story presenting the fundamental ideas of zero-knowledge proofs, first published in 1990 by Jean-Jacques Quisquater and others in their paper "How to Explain Zero-Knowledge Protocols to Your Children".[4] Using the common Alice and Bob anthropomorphic thought experiment placeholders, the two parties in a zero-knowledge proof are Peggy as the prover of the statement, and Victor, the verifier of the statement. In this story, Peggy has uncovered the secret word used to open a magic door in a cave. The cave is shaped like a ring, with the entrance on one side and the magic door blocking the opposite side. Victor wants to know whether Peggy knows the secret word; but Peggy, being a very private person, does not want to reveal her knowledge (the secret word) to Victor or to reveal the fact of her knowledge to the world in general. They label the left and right paths from the entrance A and B. First, Victor waits outside the cave as Peggy goes in. Peggy takes either path A or B; Victor is not allowed to see which path she takes. Then, Victor enters the cave and shouts the name of the path he wants her to use to return, either A or B, chosen at random. Providing she really does know the magic word, this is easy: she opens the door, if necessary, and returns along the desired path. However, suppose she did not know the word. Then, she would only be able to return by the named path if Victor were to give the name of the same path by which she had entered. Since Victor would choose A or B at random, she would have a 50% chance of guessing correctly. If they were to repeat this trick many times, say 20 times in a row, her chance of successfully anticipating all of Victor's requests would become very small (1 in 220, or very roughly 1 in a million). Thus, if Peggy repeatedly appears at the exit Victor names, he can conclude that it is extremely probable that Peggy does, in fact, know the secret word. One side note with respect to third-party observers: even if Victor is wearing a hidden camera that records the whole transaction, the only thing the camera will record is in one case Victor shouting "A!" and Peggy appearing at A or in the other case Victor shouting "B!" and Peggy appearing at B. A recording of this type would be trivial for any two people to fake (requiring only that Peggy and Victor agree beforehand on the sequence of A's and B's that Victor will shout). Such a recording will certainly never be convincing to anyone but the original participants. In fact, even a person who was present as an observer at the original experiment would be unconvinced, since Victor and Peggy might have orchestrated the whole "experiment" from start to finish. Further notice that if Victor chooses his A's and B's by flipping a coin on-camera, this protocol loses its zero-knowledge property; the on-camera coin flip would probably be convincing to any person watching the recording later. Thus, although this does not reveal the secret word to Victor, it does make it possible for Victor to convince the world in general that Peggy has that knowledge—counter to Peggy's stated wishes. However, digital cryptography generally "flips coins" by relying on a pseudo-random number generator, which is akin to a coin with a fixed pattern of heads and tails known only to the coin's owner. If Victor's coin behaved this way, then again it would be possible for Victor and Peggy to have faked the "experiment", so using a pseudo-random number generator would not reveal Peggy's knowledge to the world in the same way that using a flipped coin would. Notice that Peggy could prove to Victor that she knows the magic word, without revealing it to him, in a single trial. If both Victor and Peggy go together to the mouth of the cave, Victor can watch Peggy go in through A and come out through B. This would prove with certainty that Peggy knows the magic word, without revealing the magic word to Victor. However, such a proof could be observed by a third party, or recorded by Victor and such a proof would be convincing to anybody. In other words, Peggy could not refute such proof by claiming she colluded with Victor, and she is therefore no longer in control of who is aware of her knowledge. Two balls and the colour-blind friend Imagine your friend "Victor" is red-green colour-blind (while you are not) and you have two balls: one red and one green, but otherwise identical. To Victor, the balls seem completely identical. Victor is skeptical that the balls are actually distinguishable. You want to prove to Victor that the balls are in fact differently-coloured, but nothing else. In particular, you do not want to reveal which ball is the red one and which is the green. Here is the proof system. You give the two balls to Victor and he puts them behind his back. Next, he takes one of the balls and brings it out from behind his back and displays it. He then places it behind his back again and then chooses to reveal just one of the two balls, picking one of the two at random with equal probability. He will ask you, "Did I switch the ball?" This whole procedure is then repeated as often as necessary. By looking at the balls' colours, you can, of course, say with certainty whether or not he switched them. On the other hand, if the balls were the same colour and hence indistinguishable, there is no way you could guess correctly with probability higher than 50%. Since the probability that you would have randomly succeeded at identifying each switch/non-switch is 50%, the probability of having randomly succeeded at all switch/non-switches approaches zero ("soundness"). If you and your friend repeat this "proof" multiple times (e.g. 20 times), your friend should become convinced ("completeness") that the balls are indeed differently coloured. The above proof is zero-knowledge because your friend never learns which ball is green and which is red; indeed, he gains no knowledge about how to distinguish the balls.[5] Definition This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources in this section. Unsourced material may be challenged and removed. Find sources: "Zero-knowledge proof" – news · newspapers · books · scholar · JSTOR (July 2022) (Learn how and when to remove this template message) A zero-knowledge proof of some statement must satisfy three properties: Completeness: if the statement is true, an honest verifier (that is, one following the protocol properly) will be convinced of this fact by an honest prover. Soundness: if the statement is false, no cheating prover can convince an honest verifier that it is true, except with some small probability. Zero-knowledge: if the statement is true, no verifier learns anything other than the fact that the statement is true. In other words, just knowing the statement (not the secret) is sufficient to imagine a scenario showing that the prover knows the secret. This is formalized by showing that every verifier has some simulator that, given only the statement to be proved (and no access to the prover), can produce a transcript that "looks like" an interaction between an honest prover and the verifier in question. The first two of these are properties of more general interactive proof systems. The third is what makes the proof zero-knowledge.[6] Zero-knowledge proofs are not proofs in the mathematical sense of the term because there is some small probability, the soundness error, that a cheating prover will be able to convince the verifier of a false statement. In other words, zero-knowledge proofs are probabilistic "proofs" rather than deterministic proofs. However, there are techniques to decrease the soundness error to negligibly small values (e.g. guessing correctly on a hundred or thousand binary decisions has a 1 / 2^100 or 1/ 2^1000 soundness error, respectively. As the number of bits increases, soundness error decreases toward zero). A formal definition of zero-knowledge has to use some computational model, the most common one being that of a Turing machine. Let P P, V V, and S S be Turing machines. An interactive proof system with ( P , V ) {\displaystyle (P,V)} for a language L L is zero-knowledge if for any probabilistic polynomial time (PPT) verifier V ^ {\hat {V}} there exists a PPT simulator S S such that ∀ x ∈ L , z ∈ { 0 , 1 } ∗ , View V ^ ⁡ [ P ( x ) ↔ V ^ ( x , z ) ] = S ( x , z ) {\displaystyle \forall x\in L,z\in \{0,1\}^{*},\operatorname {View} _{\hat {V}}\left[P(x)\leftrightarrow {\hat {V}}(x,z)\right]=S(x,z)} where View V ^ ⁡ [ P ( x ) ↔ V ^ ( x , z ) ] {\displaystyle \operatorname {View} _{\hat {V}}\left[P(x)\leftrightarrow {\hat {V}}(x,z)\right]} is a record of the interactions between P ( x ) P(x) and V ^ ( x , z ) {\displaystyle {\hat {V}}(x,z)}. The prover P P is modeled as having unlimited computation power (in practice, P P usually is a probabilistic Turing machine). Intuitively, the definition states that an interactive proof system ( P , V ) {\displaystyle (P,V)} is zero-knowledge if for any verifier V ^ {\hat {V}} there exists an efficient simulator S S (depending on V ^ {\hat {V}}) that can reproduce the conversation between P P and V ^ {\hat {V}} on any given input. The auxiliary string z z in the definition plays the role of "prior knowledge" (including the random coins of V ^ {\hat {V}}). The definition implies that V ^ {\hat {V}} cannot use any prior knowledge string z z to mine information out of its conversation with P P, because if S S is also given this prior knowledge then it can reproduce the conversation between V ^ {\hat {V}} and P P just as before.[citation needed] The definition given is that of perfect zero-knowledge. Computational zero-knowledge is obtained by requiring that the views of the verifier V ^ {\hat {V}} and the simulator are only computationally indistinguishable, given the auxiliary string.[citation needed] Practical examples Discrete log of a given value We can apply these ideas to a more realistic cryptography application. Peggy wants to prove to Victor that she knows the discrete log of a given value in a given group.[7] For example, given a value y y, a large prime p p and a generator g g, she wants to prove that she knows a value x x such that g x mod p = y {\displaystyle g^{x}{\bmod {p}}=y}, without revealing x x. Indeed, knowledge of x x could be used as a proof of identity, in that Peggy could have such knowledge because she chose a random value x x that she didn't reveal to anyone, computed y = g x mod p {\displaystyle y=g^{x}{\bmod {p}}} and distributed the value of y y to all potential verifiers, such that at a later time, proving knowledge of x x is equivalent to proving identity as Peggy. The protocol proceeds as follows: in each round, Peggy generates a random number r r, computes C = g r mod p {\displaystyle C=g^{r}{\bmod {p}}} and discloses this to Victor. After receiving C C, Victor randomly issues one of the following two requests: he either requests that Peggy discloses the value of r r, or the value of ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}}. With either answer, Peggy is only disclosing a random value, so no information is disclosed by a correct execution of one round of the protocol. Victor can verify either answer; if he requested r r, he can then compute g r mod p {\displaystyle g^{r}{\bmod {p}}} and verify that it matches C C. If he requested ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}}, he can verify that C C is consistent with this, by computing g ( x + r ) mod ( p − 1 ) mod p {\displaystyle g^{(x+r){\bmod {(p-1)}}}{\bmod {p}}} and verifying that it matches ( C ⋅ y ) mod p {\displaystyle (C\cdot y){\bmod {p}}}. If Peggy indeed knows the value of x x, she can respond to either one of Victor's possible challenges. If Peggy knew or could guess which challenge Victor is going to issue, then she could easily cheat and convince Victor that she knows x x when she does not: if she knows that Victor is going to request r r, then she proceeds normally: she picks r r, computes C = g r mod p {\displaystyle C=g^{r}{\bmod {p}}} and discloses C C to Victor; she will be able to respond to Victor's challenge. On the other hand, if she knows that Victor will request ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}}, then she picks a random value r ′ r', computes C ′ = g r ′ ⋅ ( g x ) − 1 mod p {\displaystyle C'=g^{r'}\cdot \left(g^{x}\right)^{-1}{\bmod {p}}}, and discloses C ′ C' to Victor as the value of C C that he is expecting. When Victor challenges her to reveal ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}}, she reveals r ′ r', for which Victor will verify consistency, since he will in turn compute g r ′ mod p {\displaystyle g^{r'}{\bmod {p}}}, which matches C ′ ⋅ y C'\cdot y, since Peggy multiplied by the modular multiplicative inverse of y y. However, if in either one of the above scenarios Victor issues a challenge other than the one she was expecting and for which she manufactured the result, then she will be unable to respond to the challenge under the assumption of infeasibility of solving the discrete log for this group. If she picked r r and disclosed C = g r mod p {\displaystyle C=g^{r}{\bmod {p}}}, then she will be unable to produce a valid ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}} that would pass Victor's verification, given that she does not know x x. And if she picked a value r ′ r' that poses as ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}}, then she would have to respond with the discrete log of the value that she disclosed – but Peggy does not know this discrete log, since the value C she disclosed was obtained through arithmetic with known values, and not by computing a power with a known exponent. Thus, a cheating prover has a 0.5 probability of successfully cheating in one round. By executing a large enough number of rounds, the probability of a cheating prover succeeding can be made arbitrarily low. Short summary Peggy proves to know the value of x (for example her password). Peggy and Victor agree on a prime p p and a generator g g of the multiplicative group of the field Z p {\displaystyle \mathbb {Z} _{p}}. Peggy calculates the value y = g x mod p {\displaystyle y=g^{x}{\bmod {p}}} and transfers the value to Victor. The following two steps are repeated a (large) number of times. Peggy repeatedly picks a random value r ∈ U [ 0 , p − 2 ] {\displaystyle r\in U[0,p-2]} and calculates C = g r mod p {\displaystyle C=g^{r}{\bmod {p}}}. She transfers the value C C to Victor. Victor asks Peggy to calculate and transfer either the value ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}} or the value r r. In the first case Victor verifies ( C ⋅ y ) mod p ≡ g ( x + r ) mod ( p − 1 ) mod p {\displaystyle (C\cdot y){\bmod {p}}\equiv g^{(x+r){\bmod {(p-1)}}}{\bmod {p}}}. In the second case he verifies C ≡ g r mod p {\displaystyle C\equiv g^{r}{\bmod {p}}}. The value ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(}}p-1)} can be seen as the encrypted value of x mod ( p − 1 ) {\displaystyle x{\bmod {(}}p-1)}. If r r is truly random, equally distributed between zero and ( p − 2 ) {\displaystyle (p-2)}, this does not leak any information about x x (see one-time pad). Hamiltonian cycle for a large graph The following scheme is due to Manuel Blum.[8] In this scenario, Peggy knows a Hamiltonian cycle for a large graph G. Victor knows G but not the cycle (e.g., Peggy has generated G and revealed it to him.) Finding a Hamiltonian cycle given a large graph is believed to be computationally infeasible, since its corresponding decision version is known to be NP-complete. Peggy will prove that she knows the cycle without simply revealing it (perhaps Victor is interested in buying it but wants verification first, or maybe Peggy is the only one who knows this information and is proving her identity to Victor). To show that Peggy knows this Hamiltonian cycle, she and Victor play several rounds of a game. At the beginning of each round, Peggy creates H, a graph which is isomorphic to G (i.e. H is just like G except that all the vertices have different names). Since it is trivial to translate a Hamiltonian cycle between isomorphic graphs with known isomorphism, if Peggy knows a Hamiltonian cycle for G she also must know one for H. Peggy commits to H. She could do so by using a cryptographic commitment scheme. Alternatively, she could number the vertices of H. Next, for each edge of H, on a small piece of paper, she writes down the two vertices that the edge joins. Then she puts all these pieces of paper face down on a table. The purpose of this commitment is that Peggy is not able to change H while, at the same time, Victor has no information about H. Victor then randomly chooses one of two questions to ask Peggy. He can either ask her to show the isomorphism between H and G (see graph isomorphism problem), or he can ask her to show a Hamiltonian cycle in H. If Peggy is asked to show that the two graphs are isomorphic, she first uncovers all of H (e.g. by turning over all pieces of papers that she put on the table) and then provides the vertex translations that map G to H. Victor can verify that they are indeed isomorphic. If Peggy is asked to prove that she knows a Hamiltonian cycle in H, she translates her Hamiltonian cycle in G onto H and only uncovers the edges on the Hamiltonian cycle. This is enough for Victor to check that H does indeed contain a Hamiltonian cycle. It is important that the commitment to the graph be such that Victor can verify, in the second case, that the cycle is really made of edges from H. This can be done by, for example, committing to every edge (or lack thereof) separately. Completeness If Peggy does know a Hamiltonian cycle in G, she can easily satisfy Victor's demand for either the graph isomorphism producing H from G (which she had committed to in the first step) or a Hamiltonian cycle in H (which she can construct by applying the isomorphism to the cycle in G). Zero-knowledge Peggy's answers do not reveal the original Hamiltonian cycle in G. Each round, Victor will learn only H's isomorphism to G or a Hamiltonian cycle in H. He would need both answers for a single H to discover the cycle in G, so the information remains unknown as long as Peggy can generate a distinct H every round. If Peggy does not know of a Hamiltonian cycle in G, but somehow knew in advance what Victor would ask to see each round then she could cheat. For example, if Peggy knew ahead of time that Victor would ask to see the Hamiltonian cycle in H then she could generate a Hamiltonian cycle for an unrelated graph. Similarly, if Peggy knew in advance that Victor would ask to see the isomorphism then she could simply generate an isomorphic graph H (in which she also does not know a Hamiltonian cycle). Victor could simulate the protocol by himself (without Peggy) because he knows what he will ask to see. Therefore, Victor gains no information about the Hamiltonian cycle in G from the information revealed in each round. Soundness If Peggy does not know the information, she can guess which question Victor will ask and generate either a graph isomorphic to G or a Hamiltonian cycle for an unrelated graph, but since she does not know a Hamiltonian cycle for G she cannot do both. With this guesswork, her chance of fooling Victor is 2−n, where n is the number of rounds. For all realistic purposes, it is infeasibly difficult to defeat a zero-knowledge proof with a reasonable number of rounds in this way. Variants of zero-knowledge Different variants of zero-knowledge can be defined by formalizing the intuitive concept of what is meant by the output of the simulator "looking like" the execution of the real proof protocol in the following ways: We speak of perfect zero-knowledge if the distributions produced by the simulator and the proof protocol are distributed exactly the same. This is for instance the case in the first example above. Statistical zero-knowledge[9] means that the distributions are not necessarily exactly the same, but they are statistically close, meaning that their statistical difference is a negligible function. We speak of computational zero-knowledge if no efficient algorithm can distinguish the two distributions. Zero knowledge types Proof of knowledge: the knowledge is hidden in the exponent like in the example shown above. Pairing based cryptography: given f(x) and f(y), without knowing x and y, it is possible to compute f(x×y). Witness indistinguishable proof: verifiers cannot know which witness is used for producing the proof. Multi-party computation: while each party can keep their respective secret, they together produce a result. Ring signature: outsiders have no idea which key is used for signing. Applications Authentication systems Research in zero-knowledge proofs has been motivated by authentication systems where one party wants to prove its identity to a second party via some secret information (such as a password) but doesn't want the second party to learn anything about this secret. This is called a "zero-knowledge proof of knowledge". However, a password is typically too small or insufficiently random to be used in many schemes for zero-knowledge proofs of knowledge. A zero-knowledge password proof is a special kind of zero-knowledge proof of knowledge that addresses the limited size of passwords.[citation needed] In April 2015, the Sigma protocol (one-out-of-many proofs) was introduced.[10] In August 2021, Cloudflare, an American web infrastructure and security company decided to use the one-out-of-many proofs mechanism for private web verification using vendor hardware.[11] Ethical behavior One of the uses of zero-knowledge proofs within cryptographic protocols is to enforce honest behavior while maintaining privacy. Roughly, the idea is to force a user to prove, using a zero-knowledge proof, that its behavior is correct according to the protocol.[12][13] Because of soundness, we know that the user must really act honestly in order to be able to provide a valid proof. Because of zero knowledge, we know that the user does not compromise the privacy of its secrets in the process of providing the proof.[citation needed] Nuclear disarmament In 2016, the Princeton Plasma Physics Laboratory and Princeton University demonstrated a technique that may have applicability to future nuclear disarmament talks. It would allow inspectors to confirm whether or not an object is indeed a nuclear weapon without recording, sharing or revealing the internal workings which might be secret.[14] Blockchains Zero-knowledge proofs were applied in the Zerocoin and Zerocash protocols, which culminated in the birth of Zcoin[15] (later rebranded as Firo in 2020)[16] and Zcash cryptocurrencies in 2016. Zerocoin has a built-in mixing model that does not trust any peers or centralised mixing providers to ensure anonymity.[15] Users can transact in a base currency and can cycle the currency into and out of Zerocoins.[17] The Zerocash protocol uses a similar model (a variant known as a non-interactive zero-knowledge proof)[18] except that it can obscure the transaction amount, while Zerocoin cannot. Given significant restrictions of transaction data on the Zerocash network, Zerocash is less prone to privacy timing attacks when compared to Zerocoin. However, this additional layer of privacy can cause potentially undetected hyperinflation of Zerocash supply because fraudulent coins cannot be tracked.[15][19] In 2018, Bulletproofs were introduced. Bulletproofs are an improvement from non-interactive zero-knowledge proof where trusted setup is not needed.[20] It was later implemented into the Mimblewimble protocol (which the Grin and Beam cryptocurrencies are based upon) and Monero cryptocurrency.[21] In 2019, Firo implemented the Sigma protocol, which is an improvement on the Zerocoin protocol without trusted setup.[22][10] In the same year, Firo introduced the Lelantus protocol, an improvement on the Sigma protocol, where the former hides the origin and amount of a transaction.[23] History Zero-knowledge proofs were first conceived in 1985 by Shafi Goldwasser, Silvio Micali, and Charles Rackoff in their paper "The Knowledge Complexity of Interactive Proof-Systems".[12] This paper introduced the IP hierarchy of interactive proof systems (see interactive proof system) and conceived the concept of knowledge complexity, a measurement of the amount of knowledge about the proof transferred from the prover to the verifier. They also gave the first zero-knowledge proof for a concrete problem, that of deciding quadratic nonresidues mod m. Together with a paper by László Babai and Shlomo Moran, this landmark paper invented interactive proof systems, for which all five authors won the first Gödel Prize in 1993. In their own words, Goldwasser, Micali, and Rackoff say: Of particular interest is the case where this additional knowledge is essentially 0 and we show that [it] is possible to interactively prove that a number is quadratic non residue mod m releasing 0 additional knowledge. This is surprising as no efficient algorithm for deciding quadratic residuosity mod m is known when m’s factorization is not given. Moreover, all known NP proofs for this problem exhibit the prime factorization of m. This indicates that adding interaction to the proving process, may decrease the amount of knowledge that must be communicated in order to prove a theorem. The quadratic nonresidue problem has both an NP and a co-NP algorithm, and so lies in the intersection of NP and co-NP. This was also true of several other problems for which zero-knowledge proofs were subsequently discovered, such as an unpublished proof system by Oded Goldreich verifying that a two-prime modulus is not a Blum integer.[24] Oded Goldreich, Silvio Micali, and Avi Wigderson took this one step further, showing that, assuming the existence of unbreakable encryption, one can create a zero-knowledge proof system for the NP-complete graph coloring problem with three colors. Since every problem in NP can be efficiently reduced to this problem, this means that, under this assumption, all problems in NP have zero-knowledge proofs.[25] The reason for the assumption is that, as in the above example, their protocols require encryption. A commonly cited sufficient condition for the existence of unbreakable encryption is the existence of one-way functions, but it is conceivable that some physical means might also achieve it. On top of this, they also showed that the graph nonisomorphism problem, the complement of the graph isomorphism problem, has a zero-knowledge proof. This problem is in co-NP, but is not currently known to be in either NP or any practical class. More generally, Russell Impagliazzo and Moti Yung as well as Ben-Or et al. would go on to show that, also assuming one-way functions or unbreakable encryption, that there are zero-knowledge proofs for all problems in IP = PSPACE, or in other words, anything that can be proved by an interactive proof system can be proved with zero knowledge.[26][27] Not liking to make unnecessary assumptions, many theorists sought a way to eliminate the necessity of one way functions. One way this was done was with multi-prover interactive proof systems (see interactive proof system), which have multiple independent provers instead of only one, allowing the verifier to "cross-examine" the provers in isolation to avoid being misled. It can be shown that, without any intractability assumptions, all languages in NP have zero-knowledge proofs in such a system.[28] It turns out that in an Internet-like setting, where multiple protocols may be executed concurrently, building zero-knowledge proofs is more challenging. The line of research investigating concurrent zero-knowledge proofs was initiated by the work of Dwork, Naor, and Sahai.[29] One particular development along these lines has been the development of witness-indistinguishable proof protocols. The property of witness-indistinguishability is related to that of zero-knowledge, yet witness-indistinguishable protocols do not suffer from the same problems of concurrent execution.[30] Another variant of zero-knowledge proofs are non-interactive zero-knowledge proofs. Blum, Feldman, and Micali showed that a common random string shared between the prover and the verifier is enough to achieve computational zero-knowledge without requiring interaction.[2][3] Zero-Knowledge Proof protocols The most popular interactive or non-interactive zero-knowledge proof (e.g., zk-SNARK) protocols can be broadly categorized in the following four categories: Succinct Non-Interactive ARguments of Knowledge (SNARK), Scalable Transparent ARgument of Knowledge (STARK), Verifiable Polynomial Delegation (VPD), and Succinct Non-interactive ARGuments (SNARG). A list of zero-knowledge proof protocols and libraries is provided below along with comparisons based on transparency, universality, plausible post-quantum security, and programming paradigm.[31] A transparent protocol is one that does not require any trusted setup and uses public randomness. A universal protocol is one that does not require a separate trusted setup for each circuit. Finally, a plausibly post-quantum protocol is one that is not susceptible to known attacks involving quantum algorithms. Zero-knowledge proof (ZKP) systems ZKP System Publication year Protocol Transparent Universal Plausibly Post-Quantum Secure Programming Paradigm Pinocchio[32] 2013 zk-SNARK No No No Procedural Geppetto[33] 2015 zk-SNARK No No No Procedural TinyRAM[34] 2013 zk-SNARK No No No Procedural Buffet[35] 2015 zk-SNARK No No No Procedural ZoKrates[36] 2018 zk-SNARK No No No Procedural xJsnark[37] 2018 zk-SNARK No No No Procedural vRAM[38] 2018 zk-SNARG No Yes No Assembly vnTinyRAM[39] 2014 zk-SNARK No Yes No Procedural MIRAGE[40] 2020 zk-SNARK No Yes No Arithmetic Circuits Sonic[41] 2019 zk-SNARK No Yes No Arithmetic Circuits Marlin[42] 2020 zk-SNARK No Yes No Arithmetic Circuits PLONK[43] 2019 zk-SNARK No Yes No Arithmetic Circuits SuperSonic[44] 2020 zk-SNARK Yes Yes No Arithmetic Circuits Bulletproofs[20] 2018 Bulletproofs Yes Yes No Arithmetic Circuits Hyrax[45] 2018 zk-SNARK Yes Yes No Arithmetic Circuits Halo[46] 2019 zk-SNARK Yes Yes No Arithmetic Circuits Virgo[47] 2020 zk-SNARK Yes Yes Yes Arithmetic Circuits Ligero[48] 2017 zk-SNARK Yes Yes Yes Arithmetic Circuits Aurora[49] 2019 zk-SNARK Yes Yes Yes Arithmetic Circuits zk-STARK[50] 2019 zk-STARK Yes Yes Yes Assembly Zilch[31] 2021 zk-STARK Yes Yes Yes Object-Oriented See also Arrow information paradox Cryptographic protocol Feige–Fiat–Shamir identification scheme Proof of knowledge Topics in cryptography Witness-indistinguishable proof Zero-knowledge password proof Non-interactive zero-knowledge proof References "What is a zero-knowledge proof and why is it useful?". 16 November 2017. 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"SNARKs for C: Verifying Program Executions Succinctly and in Zero Knowledge". Advances in Cryptology – CRYPTO 2013. Lecture Notes in Computer Science. 8043: 90–108. doi:10.1007/978-3-642-40084-1_6. hdl:1721.1/87953. ISBN 978-3-642-40083-4. Wahby, Riad S.; Setty, Srinath; Ren, Zuocheng; Blumberg, Andrew J.; Walfish, Michael (2015). "Efficient RAM and Control Flow in Verifiable Outsourced Computation". Proceedings 2015 Network and Distributed System Security Symposium. doi:10.14722/ndss.2015.23097. ISBN 978-1-891562-38-9. Eberhardt, Jacob; Tai, Stefan (July 2018). "ZoKrates - Scalable Privacy-Preserving Off-Chain Computations". 2018 IEEE International Conference on Internet of Things (IThings) and IEEE Green Computing and Communications (GreenCom) and IEEE Cyber, Physical and Social Computing (CPSCom) and IEEE Smart Data (SmartData): 1084–1091. doi:10.1109/Cybermatics_2018.2018.00199. ISBN 978-1-5386-7975-3. S2CID 49473237. Kosba, Ahmed; Papamanthou, Charalampos; Shi, Elaine (May 2018). "xJsnark: A Framework for Efficient Verifiable Computation". 2018 IEEE Symposium on Security and Privacy (SP): 944–961. doi:10.1109/SP.2018.00018. ISBN 978-1-5386-4353-2. Zhang, Yupeng; Genkin, Daniel; Katz, Jonathan; Papadopoulos, Dimitrios; Papamanthou, Charalampos (May 2018). "vRAM: Faster Verifiable RAM with Program-Independent Preprocessing". 2018 IEEE Symposium on Security and Privacy (SP): 908–925. doi:10.1109/SP.2018.00013. ISBN 978-1-5386-4353-2. Ben-Sasson, Eli; Chiesa, Alessandro; Tromer, Eran; Virza, Madars (20 August 2014). "Succinct non-interactive zero knowledge for a von Neumann architecture". Proceedings of the 23rd USENIX Conference on Security Symposium. USENIX Association: 781–796. ISBN 9781931971157. Kosba, Ahmed; Papadopoulos, Dimitrios; Papamanthou, Charalampos; Song, Dawn (2020). "MIRAGE: Succinct Arguments for Randomized Algorithms with Applications to Universal zk-SNARKs". Cryptology ePrint Archive. Maller, Mary; Bowe, Sean; Kohlweiss, Markulf; Meiklejohn, Sarah (6 November 2019). "Sonic: Zero-Knowledge SNARKs from Linear-Size Universal and Updatable Structured Reference Strings". Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security. Association for Computing Machinery: 2111–2128. doi:10.1145/3319535.3339817. hdl:20.500.11820/739b94f1-54f0-4ec3-9644-3c95eea1e8f5. S2CID 242772913. Chiesa, Alessandro; Hu, Yuncong; Maller, Mary; Mishra, Pratyush; Vesely, Noah; Ward, Nicholas (2020). "Marlin: Preprocessing zkSNARKs with Universal and Updatable SRS". Advances in Cryptology – EUROCRYPT 2020. Lecture Notes in Computer Science. Springer International Publishing. 12105: 738–768. doi:10.1007/978-3-030-45721-1_26. ISBN 978-3-030-45720-4. S2CID 204772154. Gabizon, Ariel; Williamson, Zachary J.; Ciobotaru, Oana (2019). "PLONK: Permutations over Lagrange-bases for Oecumenical Noninteractive arguments of Knowledge". Cryptology ePrint Archive. Bünz, Benedikt; Fisch, Ben; Szepieniec, Alan (2020). "Transparent SNARKs from DARK Compilers". Advances in Cryptology – EUROCRYPT 2020. Lecture Notes in Computer Science. Springer International Publishing. 12105: 677–706. doi:10.1007/978-3-030-45721-1_24. ISBN 978-3-030-45720-4. S2CID 204892714. Wahby, Riad S.; Tzialla, Ioanna; Shelat, Abhi; Thaler, Justin; Walfish, Michael (May 2018). "Doubly-Efficient zkSNARKs Without Trusted Setup". 2018 IEEE Symposium on Security and Privacy (SP): 926–943. doi:10.1109/SP.2018.00060. ISBN 978-1-5386-4353-2. Bowe, Sean; Grigg, Jack; Hopwood, Daira (2019). "Recursive Proof Composition without a Trusted Setup". Cryptology ePrint Archive. Zhang, Jiaheng; Xie, Tiancheng; Zhang, Yupeng; Song, Dawn (May 2020). "Transparent Polynomial Delegation and Its Applications to Zero Knowledge Proof". 2020 IEEE Symposium on Security and Privacy (SP): 859–876. doi:10.1109/SP40000.2020.00052. ISBN 978-1-7281-3497-0. Ames, Scott; Hazay, Carmit; Ishai, Yuval; Venkitasubramaniam, Muthuramakrishnan (30 October 2017). "Ligero: Lightweight Sublinear Arguments Without a Trusted Setup". Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security. Association for Computing Machinery: 2087–2104. doi:10.1145/3133956.3134104. ISBN 9781450349468. S2CID 5348527. Ben-Sasson, Eli; Chiesa, Alessandro; Riabzev, Michael; Spooner, Nicholas; Virza, Madars; Ward, Nicholas P. (2019). "Aurora: Transparent Succinct Arguments for R1CS". Advances in Cryptology – EUROCRYPT 2019. Lecture Notes in Computer Science. Springer International Publishing. 11476: 103–128. doi:10.1007/978-3-030-17653-2_4. ISBN 978-3-030-17652-5. S2CID 52832327. Ben-Sasson, Eli; Bentov, Iddo; Horesh, Yinon; Riabzev, Michael (2019). "Scalable Zero Knowledge with No Trusted Setup". Advances in Cryptology – CRYPTO 2019. Lecture Notes in Computer Science. Springer International Publishing. 11694: 701–732. doi:10.1007/978-3-030-26954-8_23. ISBN 978-3-030-26953-1. S2CID 199501907. Categories: Theory of cryptographyZero-knowledge protocols https://en.wikipedia.org/wiki/Zero-knowledge_proof https://en.wikipedia.org/wiki/List_of_knowledge_deities Category:Zero-knowledge protocols Category Talk Read Edit View history Tools Help From Wikipedia, the free encyclopedia The main article for this category is Zero-knowledge protocol. Pages in category "Zero-knowledge protocols" The following 6 pages are in this category, out of 6 total. This list may not reflect recent changes. A Anonymous veto network C Commitment scheme D Dining cryptographers problem F Feige–Fiat–Shamir identification scheme O Open vote network Z Zero-knowledge proof Categories: Asymmetric-key algorithmsCryptographic protocols https://en.wikipedia.org/wiki/Category:Zero-knowledge_protocols https://en.wikipedia.org/wiki/Law_of_Demeter https://en.wikipedia.org/wiki/Slack_(software) https://en.wikipedia.org/wiki/Uncommon_Knowledge https://en.wikipedia.org/wiki/Threshold_knowledge https://en.wikipedia.org/wiki/Timeline_of_knowledge_about_galaxies,_clusters_of_galaxies,_and_large-scale_structure https://en.wikipedia.org/wiki/Innatism https://en.wikipedia.org/wiki/Rationalism#The_innate_knowledge_thesis https://en.wikipedia.org/wiki/House_of_Knowledge https://en.wikipedia.org/wiki/Knowledge_Quarter https://en.wikipedia.org/wiki/Consilience_(book) https://en.wikipedia.org/wiki/Socrates#Virtue_and_knowledge https://en.wikipedia.org/wiki/Relativism https://en.wikipedia.org/wiki/Vidya_(philosophy) https://en.wikipedia.org/wiki/Knowledge_production_modes https://en.wikipedia.org/wiki/Local_knowledge_problem https://en.wikipedia.org/wiki/The_Postmodern_Condition https://en.wikipedia.org/wiki/Knowledge_translation https://en.wikipedia.org/wiki/Braiding_Sweetgrass https://en.wikipedia.org/wiki/Democratization_of_knowledge https://en.wikipedia.org/wiki/Knowledge_gap_hypothesis https://en.wikipedia.org/wiki/Certainty https://en.wikipedia.org/wiki/STOCK_Act https://en.wikipedia.org/wiki/Knowledge_Is_King https://en.wikipedia.org/wiki/Semantic_Scholar https://en.wikipedia.org/wiki/Knowledge_broker https://en.wikipedia.org/wiki/Route_knowledge https://en.wikipedia.org/wiki/Knowledge-based_processor https://en.wikipedia.org/wiki/Forbidden_knowledge https://en.wikipedia.org/wiki/Wikidata https://en.wikipedia.org/wiki/Encyclopedic_knowledge https://en.wikipedia.org/wiki/Knowledge_space https://en.wikipedia.org/wiki/Knowledge_level https://en.wikipedia.org/wiki/The_Sword_of_Knowledge https://en.wikipedia.org/wiki/Schema_(psychology) https://en.wikipedia.org/wiki/Pedagogy https://en.wikipedia.org/wiki/Experiential_knowledge https://en.wikipedia.org/wiki/Postmodernism https://en.wikipedia.org/wiki/Core_Knowledge https://en.wikipedia.org/wiki/Prop%C3%A6dia#Outline_of_Knowledge https://en.wikipedia.org/wiki/Karl_Popper https://en.wikipedia.org/wiki/Michel_Foucault https://en.wikipedia.org/wiki/Access_to_Knowledge_movement https://en.wikipedia.org/wiki/Hutter_Prize https://en.wikipedia.org/wiki/SECI_model_of_knowledge_dimensions https://en.wikipedia.org/wiki/Consilience_(book) https://en.wikipedia.org/wiki/Everyman_(15th-century_play) https://en.wikipedia.org/wiki/Abhij%C3%B1%C4%81 https://en.wikipedia.org/wiki/Ismail_al-Jazari https://en.wikipedia.org/wiki/Traditional_ecological_knowledge https://en.wikipedia.org/wiki/Pseudoscience https://en.wikipedia.org/wiki/Empiricism https://en.wikipedia.org/wiki/Scientist https://en.wikipedia.org/wiki/An_Essay_on_Criticism https://en.wikipedia.org/wiki/Ornithology#Early_knowledge_and_study https://en.wikipedia.org/wiki/Technological_pedagogical_content_knowledge https://en.wikipedia.org/wiki/Knowledge_Generation_Bureau https://en.wikipedia.org/wiki/University https://en.wikipedia.org/wiki/Knowledge_compilation https://en.wikipedia.org/wiki/Sherlock_Holmes#Knowledge_and_skills https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction https://en.wikipedia.org/wiki/Tree_of_Knowledge_(Australia) https://en.wikipedia.org/wiki/Vocabulary#Productive_and_receptive_knowledge https://en.wikipedia.org/wiki/Appropriation_of_knowledge https://en.wikipedia.org/wiki/Skepticism https://en.wikipedia.org/wiki/Bioprospecting https://en.wikipedia.org/wiki/Frame_(artificial_intelligence)#Frame_language https://en.wikipedia.org/wiki/Mathematical_knowledge_management https://en.wikipedia.org/wiki/Texas_Assessment_of_Knowledge_and_Skills https://en.wikipedia.org/wiki/Augustine_of_Hippo#Natural_knowledge_and_biblical_interpretation https://en.wikipedia.org/wiki/W._Edwards_Deming#The_Deming_System_of_Profound_Knowledge https://en.wikipedia.org/wiki/Follow-the-sun https://en.wikipedia.org/wiki/Non-interactive_zero-knowledge_proof https://en.wikipedia.org/wiki/Terry_Scott_Taylor#Knowledge_&_Innocence https://en.wikipedia.org/wiki/Omniscience https://en.wikipedia.org/wiki/Invention_of_Knowledge https://en.wikipedia.org/wiki/Theaetetus_(dialogue)#Protagoras%27_theory_of_knowledge https://en.wikipedia.org/wiki/Knowledge_neglect https://en.wikipedia.org/wiki/Scientia_sacra https://en.wikipedia.org/wiki/Knowledge_and_Decisions https://en.wikipedia.org/wiki/Proof_of_knowledge https://en.wikipedia.org/wiki/Factual_relativism https://en.wikipedia.org/wiki/Knowledge_Query_and_Manipulation_Language https://en.wikipedia.org/wiki/Knowledge-based_engineering https://en.wikipedia.org/wiki/Multi-factor_authentication https://en.wikipedia.org/wiki/Knowledge_survey https://en.wikipedia.org/wiki/Intellectual_capital https://en.wikipedia.org/wiki/Transcendentalism#Transcendental_knowledge https://en.wikipedia.org/wiki/Theory_of_knowledge_(disambiguation) https://en.wikipedia.org/wiki/A_Culture_of_Conspiracy https://en.wikipedia.org/wiki/A_Treatise_Concerning_the_Principles_of_Human_Knowledge https://en.wikipedia.org/wiki/Objectivity_(philosophy) https://en.wikipedia.org/wiki/Knowledge_regime https://en.wikipedia.org/wiki/The_Social_Construction_of_Reality https://en.wikipedia.org/wiki/Francis_Bacon#Organization_of_knowledge https://en.wikipedia.org/wiki/Knowledge-based_recommender_system https://en.wikipedia.org/wiki/Traditional_medicine#Knowledge_transmission_and_creation https://en.wikipedia.org/wiki/Information_silo https://en.wikipedia.org/wiki/World_Bank#Global_Operations_Knowledge_Management_Unit https://en.wikipedia.org/wiki/Philosophical_skepticism https://en.wikipedia.org/wiki/The_Knowledge:_How_to_Rebuild_Our_World_from_Scratch https://en.wikipedia.org/wiki/Bayes%27_theorem?wprov=srpw1_412 https://en.wikipedia.org/wiki/Mathematician https://en.wikipedia.org/wiki/Zoology https://en.wikipedia.org/wiki/Adam_and_Eve https://en.wikipedia.org/wiki/Foundations_of_the_Science_of_Knowledge https://en.wikipedia.org/wiki/Unity_of_science https://en.wikipedia.org/wiki/Nihilism https://en.wikipedia.org/wiki/Tabula_rasa Meaning of knowledge Linguistic According to the Oxford English Dictionary, the word knowledge refers to "Facts, information, and skills acquired through experience or education; the theoretical or practical understanding of a subject." "In this work on the concept of knowledge, Franz Rosenthal collected a number of definitions of 'ilm, organizing them according to what he saw as their essential elements (admitting that the list was ahistorical and did not necessarily conform to categories the medieval Muslim scholars themselves would have used). Among these definitions, we find the following: Knowledge is the process of knowing, and identical with the knower and the known. Knowledge is that through which one knows. Knowledge is that through which the essence is knowing. Knowledge is that through which the knower is knowing. Knowledge is that which necessitates for him in whom it subsists the name of knower. Knowledge is that which necessitates that he in whom it subsists is knowing. Knowledge is that which necessitates that he in whom it resides (mahall) is knowing. Knowledge stands for ( 'ibarah 'an) the object known ( 'al-ma lum). Knowledge is but the concepts known ( 'al-ma ani al-ma luma). Knowledge is the mentally existing object."[1] Islamic meaning Knowledge in the Western world means information about something, divine or corporeal, while In Islamic point of view 'ilm is an all-embracing term covering theory, action and education, it is not confined to the acquisition of knowledge only, but also embraces socio-political and moral aspects.it requires insight, commitment to the goals of Islam and for the believers to act upon their belief.[2] Also it is reported in hadith that "Knowledge is not extensive learning. Rather, it is a light that God casts in the heart of whomever He wills." [3] https://en.wikipedia.org/wiki/Ilm_(Arabic)#Meaning_of_knowledge https://en.wikipedia.org/wiki/Scientific_Knowledge_and_Its_Social_Problems https://en.wikipedia.org/wiki/Citation https://en.wikipedia.org/wiki/Problem_solving https://en.wikipedia.org/wiki/Modern_flat_Earth_beliefs https://en.wikipedia.org/wiki/Generosity#In_knowledge https://en.wikipedia.org/wiki/Amnesia https://en.wikipedia.org/wiki/Spherical_Earth https://en.wikipedia.org/wiki/Library_Genesis https://en.wikipedia.org/wiki/Third_eye https://en.wikipedia.org/wiki/International_Service_for_the_Acquisition_of_Agri-biotech_Applications#Global_Knowledge_Center_on_Crop_Biotechnology https://en.wikipedia.org/wiki/WolframAlpha https://en.wikipedia.org/wiki/Knowledge-based_authentication https://en.wikipedia.org/wiki/Pre-Socratic_philosophy#Knowledge https://en.wikipedia.org/wiki/Reinforcement_learning https://en.wikipedia.org/wiki/Magician_(fantasy) https://en.wikipedia.org/wiki/Physicist https://en.wikipedia.org/wiki/Test_of_Economic_Knowledge https://en.wikipedia.org/wiki/Precognition https://en.wikipedia.org/wiki/Basic_research https://en.wikipedia.org/wiki/Methodology https://en.wikipedia.org/wiki/Experience https://en.wikipedia.org/wiki/Mens_rea https://en.wikipedia.org/wiki/Schaff%E2%80%93Herzog_Encyclopedia_of_Religious_Knowledge https://en.wikipedia.org/wiki/The_Secret_Knowledge https://en.wikipedia.org/wiki/Penny_Cyclopaedia#National_Cyclopedia_of_Useful_Knowledge https://en.wikipedia.org/wiki/Non-monotonic_logic https://en.wikipedia.org/wiki/Sustainable_Development_Goals https://en.wikipedia.org/wiki/Cognitive_psychology https://en.wikipedia.org/wiki/Human_behavior https://en.wikipedia.org/wiki/Coloniality_of_power#Systems_of_knowledge https://en.wikipedia.org/wiki/Printing https://en.wikipedia.org/wiki/The_Way_to_Divine_Knowledge https://en.wikipedia.org/wiki/Waldwissen https://en.wikipedia.org/wiki/Non-disclosure_agreement https://en.wikipedia.org/wiki/Lexicon https://en.wikipedia.org/wiki/Noble_Eightfold_Path https://en.wikipedia.org/wiki/If_a_tree_falls_in_a_forest#Knowledge_of_the_unobserved_world https://en.wikipedia.org/wiki/History_of_science https://en.wikipedia.org/wiki/Hematology https://en.wikipedia.org/wiki/Justification_(epistemology)#Justification_and_knowledge https://en.wikipedia.org/wiki/Discourse https://en.wikipedia.org/wiki/Unity_of_knowledge_and_action https://en.wikipedia.org/wiki/Tartary https://en.wikipedia.org/wiki/Philanthropedia https://en.wikipedia.org/wiki/Visualization_(graphics) https://en.wikipedia.org/wiki/Nightingale_Pledge https://en.wikipedia.org/wiki/Doctor_of_Science https://en.wikipedia.org/wiki/Expert_system https://en.wikipedia.org/wiki/Walker%27s_Hibernian_Magazine https://en.wikipedia.org/wiki/Critical_theory https://en.wikipedia.org/wiki/Scientific_management https://en.wikipedia.org/wiki/Autodidacticism https://en.wikipedia.org/wiki/Occult https://en.wikipedia.org/wiki/FlatWorld https://en.wikipedia.org/wiki/Paradigm_shift https://en.wikipedia.org/wiki/History_of_mathematics https://en.wikipedia.org/wiki/War_for_talent#Knowledge_work https://en.wikipedia.org/wiki/Technocracy https://en.wikipedia.org/wiki/Supernatural https://en.wikipedia.org/wiki/Fall_of_man https://en.wikipedia.org/wiki/Anthroposophy#Spiritual_knowledge_and_freedom https://en.wikipedia.org/wiki/Aladdin_Knowledge_Systems https://en.wikipedia.org/wiki/Streetwise https://en.wikipedia.org/wiki/List_of_musical_instruments https://en.wikipedia.org/wiki/Celestial_Emporium_of_Benevolent_Knowledge https://en.wikipedia.org/wiki/Analytic_philosophy https://en.wikipedia.org/wiki/Maxim_(philosophy)#Personal_knowledge https://en.wikipedia.org/wiki/Second_language#Depth_of_knowledge https://en.wikipedia.org/wiki/Moksha https://en.wikipedia.org/wiki/Mutual_knowledge https://en.wikipedia.org/wiki/Diffusion_of_innovations https://en.wikipedia.org/wiki/Hinterland#Breadth_of_knowledge https://en.wikipedia.org/wiki/Rhetoric#Knowledge https://en.wikipedia.org/wiki/Consistency_(knowledge_bases) https://en.wikipedia.org/wiki/Innocence#In_relation_to_knowledge https://en.wikipedia.org/wiki/World_of_Knowledge https://en.wikipedia.org/wiki/Intelligence_agency https://en.wikipedia.org/wiki/Contamination https://en.wikipedia.org/wiki/Positivism https://en.wikipedia.org/wiki/Hockney%E2%80%93Falco_thesis https://en.wikipedia.org/wiki/Paradise_Lost https://en.wikipedia.org/wiki/Ethics https://en.wikipedia.org/wiki/Engineering https://en.wikipedia.org/wiki/School https://en.wikipedia.org/wiki/Christian_mysticism#False_spiritual_knowledge https://en.wikipedia.org/wiki/Human%E2%80%93computer_interaction#Knowledge-driven_human%E2%80%93computer_interaction https://en.wikipedia.org/wiki/Notice#Notice_and_knowledge https://en.wikipedia.org/wiki/Falsifiability https://en.wikipedia.org/wiki/Fionn_mac_Cumhaill https://en.wikipedia.org/wiki/Outline_of_epistemology https://en.wikipedia.org/wiki/Cognitive_robotics#Knowledge_acquisition https://en.wikipedia.org/wiki/Writing#Scientific_and_scholarly_knowledge_production https://en.wikipedia.org/wiki/Is%E2%80%93ought_problem https://en.wikipedia.org/wiki/The_Degrees_of_Knowledge https://en.wikipedia.org/wiki/Genetic_epistemology#Types_of_knowledge https://en.wikipedia.org/wiki/The_Universal_Magazine_of_Knowledge_and_Pleasure https://en.wikipedia.org/wiki/Divergent_(novel)#Social_structure_and_knowledge https://en.wikipedia.org/wiki/Anti-pattern https://en.wikipedia.org/wiki/Compendium https://en.wikipedia.org/wiki/Compendium https://en.wikipedia.org/wiki/Evaluation https://en.wikipedia.org/wiki/Postcolonialism https://en.wikipedia.org/wiki/American_Philosophical_Society https://en.wikipedia.org/wiki/Reference https://en.wikipedia.org/wiki/Patent_box https://en.wikipedia.org/wiki/KNOMAD https://en.wikipedia.org/wiki/Ebers_Papyrus#Medical_knowledge https://en.wikipedia.org/wiki/Black-box_testing https://en.wikipedia.org/wiki/Perennial_philosophy https://en.wikipedia.org/wiki/Prisca_theologia https://en.wikipedia.org/wiki/Neoplatonism https://en.wikipedia.org/wiki/Hellenistic_philosophy https://en.wikipedia.org/wiki/Alexander_the_Great https://en.wikipedia.org/wiki/Achaemenid_Empire https://en.wikipedia.org/wiki/Laplace%27s_demon https://en.wikipedia.org/wiki/Idealism https://en.wikipedia.org/wiki/Classification https://en.wikipedia.org/wiki/Uncertainty https://en.wikipedia.org/wiki/Reality https://en.wikipedia.org/wiki/World_Intellectual_Property_Organization#Genetic_resources%2C_traditional_knowledge_and_traditional_cultural_expressions https://en.wikipedia.org/wiki/Knowledge_divide https://en.wikipedia.org/wiki/Computable_knowledge https://en.wikipedia.org/wiki/Gunnery_sergeant https://en.wikipedia.org/wiki/House_of_Wisdom https://en.wikipedia.org/wiki/Post-structuralism https://en.wikipedia.org/wiki/All_the_Knowledge_in_the_World https://en.wikipedia.org/wiki/Apocalypse_of_Adam https://en.wikipedia.org/wiki/Information_retrieval https://en.wikipedia.org/wiki/Scientism https://en.wikipedia.org/wiki/Human_settlement https://en.wikipedia.org/wiki/Akrasia https://en.wikipedia.org/wiki/Worldview https://en.wikipedia.org/wiki/Sophist https://en.wikipedia.org/wiki/Intellectual https://en.wikipedia.org/wiki/Knowledge_by_presence https://en.wikipedia.org/wiki/Science_and_technology_studies https://en.wikipedia.org/wiki/The_Open_Source_Definition#Open_Knowledge https://en.wikipedia.org/wiki/Philosophy_of_education https://en.wikipedia.org/wiki/System_administrator https://en.wikipedia.org/wiki/Logic_programming#Knowledge_representation https://en.wikipedia.org/wiki/Three_Sovereigns_and_Five_Emperors https://en.wikipedia.org/wiki/Old_wives%27_tale https://en.wikipedia.org/wiki/Children%27s_use_of_information#The_origins_of_knowledge https://en.wikipedia.org/wiki/An_Essay_Concerning_Human_Understanding https://en.wikipedia.org/wiki/Sheja_Dz%C3%B6 https://en.wikipedia.org/wiki/Second_modernity https://en.wikipedia.org/wiki/Phenomenology_(sociology) https://en.wikipedia.org/wiki/The_Open_Source_Definition

Category:Phonetic transcription symbols

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From Wikipedia, the free encyclopedia

Wikimedia Commons has media related to Phonetic transcription symbols.

For more information, see phonetic transcription.

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Pages in category "Phonetic transcription symbols"

The following 109 pages are in this category, out of 109 total. This list may not reflect recent changes.

A

• Ȧ
• Ă
• Ā
• Ã
• Æ
• Latin alpha

B

• Ɓ
• Ƀ
• Small capital B
• Beta
• Bilabial click

C

• Ç
• Ć
• Ċ
• Č
• Ƈ
• Stretched C
• Ȼ
• C with bar
• Chi (letter)
• Click letter

D

• Ḍ
• African D
• Ɗ
• D with hook and tail
• D with stroke
• Eth
• Db ligature
• Double grave accent

E

• Ẽ
• Ə
• Eng (letter)
• Latin epsilon

G

• Ǧ
• Ġ
• Insular G
• Ɠ
• Glottal stop (letter)
• Gamma
• Latin gamma

ɡ

• ꬶ

H

• Ḫ
• Heng (letter)
• H with stroke
• Turned h with fishhook
• Ḥ

I

• Ɨ
• Ɪ
• Latin iota

J

• J̌

K

• K with diagonal stroke
• Ƙ
• K with stroke
• K with stroke and diagonal stroke

L

• Ł
• Barred lambda
• Latin beta
• Latin turned alpha

M

• Ɱ
• Modifier letter left half ring
• Modifier letter right half ring

N

• Ñ
• N with long right leg
• Ɲ

O

• Ɵ
• Ö
• Ǫ
• Ø
• Œ
• ⱺ
• Open O

P

• P with stroke
• Ƥ
• Palatal hook
• Phonetic Symbol Guide

Q

• Q with stroke
• Qp ligature

R

• Ȓ
• R with tail

S

• S͎
• S with swash tail
• Š
• Ṡ
• S̀
• Esh (letter)

T

• Ƭ
• Ʈ
• Theta
• Tie (typography)
• Turned A
• Turned h

U

• U bar
• Ŭ

V

• V with diagonal stroke
• Ʋ
• Turned v
• V with curl
• Voiced labiodental flap

W

• Ɯ

X

• X̣

Y

• Ý
• Ÿ (vowel)
• Yogh

Z

• Z with swash tail
• Ezh
• Ź
• Ž
• Z̀
• Ǯ

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• Phonetic alphabets

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https://en.wikipedia.org/wiki/Category:Phonetic_transcription_symbols

In linguistics, a count noun (also countable noun) is a noun that can be modified by a quantity and that occurs in both singular and plural forms, and that can co-occur with quantificational determiners like every, each, several, etc. A mass noun has none of these properties: It cannot be modified by a number, cannot occur in plural, and cannot co-occur with quantificational determiners. 

https://en.wikipedia.org/wiki/Count_noun

A determiner, also called determinative (abbreviated DET), is a word, phrase, or affix that occurs together with a noun or noun phrase and generally serves to express the reference of that noun or noun phrase in the context. That is, a determiner may indicate whether the noun is referring to a definite or indefinite element of a class, to a closer or more distant element, to an element belonging to a specified person or thing, to a particular number or quantity, etc. Common kinds of determiners include definite and indefinite articles (the, a), demonstratives (this, that), possessive determiners (my, their), cardinal numerals (one, two), quantifiers (many, both), distributive determiners (each, every), and interrogative determiners (which, what). 

For the written element in logographic scripts, see Determinative.

 

https://en.wikipedia.org/wiki/Determiner

 

 

In linguistics, definiteness is a semantic feature of noun phrases, distinguishing between referents or senses that are identifiable in a given context (definite noun phrases) and those which are not (indefinite noun phrases). The prototypical definite noun phrase picks out a unique, familiar, specific referent such as the sun or Australia, as opposed to indefinite examples like an idea or some fish.

There is considerable variation in the expression of definiteness across languages, and some languages such as Japanese do not generally mark it so that the same expression could be definite in some contexts and indefinite in others. In other languages, such as English, it is usually marked by the selection of determiner (e.g., the vs a). In still other languages, such as Danish, definiteness is marked morphologically. 

https://en.wikipedia.org/wiki/Definiteness

 

 

Iron meteorites, also called siderites or ferrous meteorites, are a type of meteorite that consist overwhelmingly of an iron–nickel alloy known as meteoric iron that usually consists of two mineral phases: kamacite and taenite. Most iron meteorites originate from cores of planetesimals,^[2] with the exception of the IIE iron meteorite group^[3]

The iron found in iron meteorites was one of the earliest sources of usable iron available to humans, due to the malleability and ductility of the meteoric iron,^[4] before the development of smelting that signaled the beginning of the Iron Age. 

Iron meteorite
— Type —
Tamentit Iron Meteorite, found in 1864 in the Sahara,[1] weighing about 500 kg (1,100 lb). On display at Vulcania park in France.

https://en.wikipedia.org/wiki/Iron_meteorite

Count-classifiers and mass-classifiers

A classifier categorizes a class of nouns by picking out some salient perceptual properties...which are permanently associated with entities named by the class of nouns; a measure word does not categorize but denotes the quantity of the entity named by a noun.

— Tai (1994, p. 2), emphasis added

Within the set of nominal classifiers, linguists generally draw a distinction between "count-classifiers" and "mass-classifiers". True count-classifiers^{[note 8]} are used for naming or counting a single count noun,^[15] and have no direct translation in English; for example, 一本书 (yì běn shū, one-CL book) can only be translated in English as "one book" or "a book".^[20] Furthermore, count-classifiers cannot be used with mass nouns: just as an English speaker cannot ordinarily say *"five muds", a Chinese speaker cannot say *五个泥 (wǔ ge nì, five-CL mud). For such mass nouns, one must use mass-classifiers.^{[15][note 9]}

Mass-classifiers (true measure words) do not pick out inherent properties of an individual noun like count-classifiers do; rather, they lump nouns into countable units. Thus, mass-classifiers can generally be used with multiple types of nouns; for example, while the mass-classifier 盒 (hé, box) can be used to count boxes of lightbulbs (一盒灯泡 yì hé dēngpào, "one box of lightbulbs") or of books (一盒教材 yì hé jiàocái, "one box of textbooks"), each of these nouns must use a different count-classifier when being counted by itself (一盏灯泡 yì zhǎn dēngpào "one lightbulb"; vs. 一本教材 yì běn jiàocái "one textbook"). While count-classifiers have no direct English translation, mass-classifiers often do: phrases with count-classifiers such as 一个人 (yí ge rén, one-CL person) can only be translated as "one person" or "a person", whereas those with mass-classifiers such as 一群人 (yì qún rén, one-crowd-person) can be translated as "a crowd of people". All languages, including English, have mass-classifiers, but count-classifiers are unique to certain "classifier languages", and are not a part of English grammar apart from a few exceptional cases such as head of livestock.^[21]

Within the range of mass-classifiers, authors have proposed subdivisions based on the manner in which a mass-classifier organizes the noun into countable units. One of these is measurement units (also called "standard measures"),^[22] which all languages must have in order to measure items; this category includes units such as kilometers, liters, or pounds^[23] (see list). Like other classifiers, these can also stand without a noun; thus, for example, 磅 (bàng, pound) may appear as both 三磅肉 (sān bàng ròu, "three pounds of meat") or just 三磅 (sān bàng, "three pounds", never *三个磅 sān ge bàng).^[24] Units of currency behave similarly: for example, 十元 (shí yuán, "ten yuan"), which is short for (for example) 十元人民币 (shí yuán rénmínbì, "ten units of renminbi"). Other proposed types of mass-classifiers include "collective"^{[25][note 10]} mass-classifiers, such as 一群人 (yì qún rén, "a crowd of people"), which group things less precisely; and "container"^[26] mass-classifiers which group things by containers they come in, as in 一碗粥 (yì wǎn zhōu, "a bowl of porridge") or 一包糖 (yì bāo táng, "a bag of sugar").

The difference between count-classifiers and mass-classifiers can be described as one of quantifying versus categorizing: in other words, mass-classifiers create a unit by which to measure something (i.e. boxes, groups, chunks, pieces, etc.), whereas count-classifiers simply name an existing item.^[27] Most words can appear with both count-classifiers and mass-classifiers; for example, pizza can be described as both 一张比萨 (yì zhāng bǐsà, "one pizza", literally "one pie of pizza"), using a count-classifier, and as 一块比萨 (yí kuài bǐsà, "one piece of pizza"), using a mass-classifier. In addition to these semantic differences, there are differences in the grammatical behaviors of count-classifiers and mass-classifiers;^[28] for example, mass-classifiers may be modified by a small set of adjectives (as in 一大群人 yí dà qún rén, "a big crowd of people"), whereas count-classifiers usually may not (for example, *一大个人 yí dà ge rén is never said for "a big person"; instead the adjective must modify the noun: 一个大人 yí ge dà rén).^[29] Another difference is that count-classifiers may often be replaced by a "general" classifier 个 (個), gè with no apparent change in meaning, whereas mass-classifiers may not.^[30] Syntacticians Lisa Cheng and Rint Sybesma propose that count-classifiers and mass-classifiers have different underlying syntactic structures, with count-classifiers forming "classifier phrases",^{[note 11]} and mass-classifiers being a sort of relative clause that only looks like a classifier phrase.^[31] The distinction between count-classifiers and mass-classifiers is often unclear, however, and other linguists have suggested that count-classifiers and mass-classifiers may not be fundamentally different. They posit that "count-classifier" and "mass-classifier" are the extremes of a continuum, with most classifiers falling somewhere in between.^[32]

Verbal classifiers

There is a set of "verbal classifiers" used specifically for counting the number of times an action occurs, rather than counting a number of items; this set includes 次 cì, 遍/徧 biàn, 回 huí, and 下 xià, which all roughly translate to "times".^[33] For example, 我去过三次北京 (wǒ qù-guo sān cì Běijīng, I go-PAST three-CL Beijing, "I have been to Beijing three times").^[34] These words can also form compound classifiers with certain nouns, as in 人次 rén cì "person-time", which can be used to count (for example) visitors to a museum in a year (where visits by the same person on different occasions are counted separately).

Another type of verbal classifier indicates the tool or implement used to perform the action. An example is found in the sentence 他踢了我一脚 tā tī le wǒ yī jiǎo "he kicked me", or more literally "he kicked me one foot". The word 脚 jiǎo, which usually serves as a simple noun meaning "foot", here functions as a verbal classifier reflecting the tool (namely the foot) used to perform the kicking action.

Relation to nouns

鱼 yú
"fish"

裤子 kùzi
"(pair of) pants"

河 hé
"river"

凳子 dèngzi
"long bench"

The above nouns denoting long or flexible objects may all appear with the classifier 条 (條) tiáo in certain dialects such as Mandarin.^[35] In Mandarin, 一条板凳 means "a CL bench", and if people want to say "a chair", 個/个 or 張/张 is used because 条 is only used for referring to relatively long things. In other dialects such as Cantonese, 條 cannot be used to refer to 櫈. Instead, 張 is used.

Different classifiers often correspond to different particular nouns. For example, books generally take the classifier 本 běn, flat objects take 张 (張) zhāng, animals take 只 (隻) zhī, machines take 台 tái, large buildings and mountains take 座 zuò, etc. Within these categories are further subdivisions—while most animals take 只 (隻) zhī, domestic animals take 头 (頭) tóu, long and flexible animals take 条 (條) tiáo, and horses take 匹 pǐ. Likewise, while long things that are flexible (such as ropes) often take 条 (條) tiáo, long things that are rigid (such as sticks) take 根 gēn, unless they are also round (like pens or cigarettes), in which case in some dialects they take 枝 zhī.^[36] Classifiers also vary in how specific they are; some (such as 朵 duǒ for flowers and other similarly clustered items) are generally only used with one type, whereas others (such as 条 (條) tiáo for long and flexible things, one-dimensional things, or abstract items like news reports)^{[note 12]} are much less restricted.^[37] Furthermore, there is not a one-to-one relationship between nouns and classifiers: the same noun may be paired with different classifiers in different situations.^[38] The specific factors that govern which classifiers are paired with which nouns have been a subject of debate among linguists.

Categories and prototypes

While mass-classifiers do not necessarily bear any semantic relationship to the noun with which they are used (e.g. box and book are not related in meaning, but one can still say "a box of books"), count-classifiers do.^[31] The precise nature of that relationship, however, is not certain, since there is so much variability in how objects may be organized and categorized by classifiers. Accounts of the semantic relationship may be grouped loosely into categorical theories, which propose that count-classifiers are matched to objects solely on the basis of inherent features of those objects (such as length or size), and prototypical theories, which propose that people learn to match a count-classifier to a specific prototypical object and to other objects that are like that prototype.^[39]

The categorical, "classical"^[40] view of classifiers was that each classifier represents a category with a set of conditions; for example, the classifier 条 (條) tiáo would represent a category defined as all objects that meet the conditions of being long, thin, and one-dimensional—and nouns using that classifier must fit all the conditions with which the category is associated. Some common semantic categories into which count-classifiers have been claimed to organize nouns include the categories of shape (long, flat, or round), size (large or small), consistency (soft or hard), animacy (human, animal, or object),^[41] and function (tools, vehicles, machines, etc.).^[42]

A mule
骡子, luózi

A donkey
驴子, lǘzi

James Tai and Wang Lianqing found that the horse classifier 匹 pǐ is sometimes used for mules and camels, but rarely for the less "horse-like" donkeys, suggesting that the choice of classifiers is influenced by prototypal closeness.^[43]

On the other hand, proponents of prototype theory propose that count-classifiers may not have innate definitions, but are associated with a noun that is prototypical of that category, and nouns that have a "family resemblance" with the prototype noun will want to use the same classifier.^{[note 13]} For example, horse in Chinese uses the classifier 匹 pǐ, as in 三匹马 (sān pǐ mǎ, "three horses")—in modern Chinese the word 匹 has no meaning. Nevertheless, nouns denoting animals that look like horses will often also use this same classifier, and native speakers have been found to be more likely to use the classifier 匹 the closer an animal looks to a horse.^[43] Furthermore, words that do not meet the "criteria" of a semantic category may still use that category because of their association with a prototype. For example, the classifier 颗 (顆) kē is used for small round items, as in 一颗子弹 (yì kē zǐdàn, "one bullet"); when words like 原子弹 (yuánzǐdàn, "atomic bomb") were later introduced into the language they also used this classifier, even though they are not small and round—therefore, their classifier must have been assigned because of the words' association with the word for bullet, which acted as a "prototype".^[44] This is an example of "generalization" from prototypes: Erbaugh has proposed that when children learn count-classifiers, they go through stages, first learning a classifier-noun pair only (such as 条鱼 tiáo yú, CL-fish), then using that classifier with multiple nouns that are similar to the prototype (such as other types of fish), then finally using that set of nouns to generalize a semantic feature associated with the classifier (such as length and flexibility) so that the classifier can then be used with new words that the person encounters.^[45]

Some classifier-noun pairings are arbitrary, or at least appear to modern speakers to have no semantic motivation.^[46] For instance, the classifier 部 bù may be used for movies and novels, but also for cars^[47] and telephones.^[48] Some of this arbitrariness may be due to what linguist James Tai refers to as "fossilization", whereby a count-classifier loses its meaning through historical changes but remains paired with some nouns. For example, the classifier 匹 pǐ used for horses is meaningless today, but in Classical Chinese may have referred to a "team of two horses",^[49] a pair of horse skeletons,^[50] or the pairing between man and horse.^{[51][note 14]} Arbitrariness may also arise when a classifier is borrowed, along with its noun, from a dialect in which it has a clear meaning to one in which it does not.^[52] In both these cases, the use of the classifier is remembered more by association with certain "prototypical" nouns (such as horse) rather than by understanding of semantic categories, and thus arbitrariness has been used as an argument in favor of the prototype theory of classifiers.^[52] Gao and Malt propose that both the category and prototype theories are correct: in their conception, some classifiers constitute "well-defined categories", others make "prototype categories", and still others are relatively arbitrary.^[53]

Neutralization

In addition to the numerous "specific" count-classifiers described above,^{[note 15]} Chinese has a "general" classifier 个 (個), pronounced gè in Mandarin.^{[note 16]} This classifier is used for people, some abstract concepts, and other words that do not have special classifiers (such as 汉堡包 hànbǎobāo "hamburger"),^[54] and may also be used as a replacement for a specific classifier such as 张 (張) zhāng or 条 (條) tiáo, especially in informal speech. In Mandarin Chinese, it has been noted as early as the 1940s that the use of 个 is increasing and that there is a general tendency towards replacing specific classifiers with it.^[55] Numerous studies have reported that both adults and children tend to use 个 when they do not know the appropriate count-classifier, and even when they do but are speaking quickly or informally.^[56] The replacement of a specific classifier with the general 个 is known as classifier neutralization^[57] ("量词个化" in Chinese, literally "classifier 个-ization"^[58]). This occurs especially often among children^[59] and aphasics (individuals with damage to language-relevant areas of the brain),^[60][61] although normal speakers also neutralize frequently. It has been reported that most speakers know the appropriate classifiers for the words they are using and believe, when asked, that those classifiers are obligatory, but nevertheless use 个 without even realizing it in actual speech.^[62] As a result, in everyday spoken Mandarin the general classifier is "hundreds of times more frequent"^[63] than the specialized ones.

Nevertheless, 个 has not completely replaced other count-classifiers, and there are still many situations in which it would be inappropriate to substitute it for the required specific classifier.^[55] There may be specific patterns behind which classifier-noun pairs may be "neutralized" to use the general classifier, and which may not. Specifically, words that are most prototypical for their categories, such as paper for the category of nouns taking the "flat/square" classifier 张 (張) zhāng, may be less likely to be said with a general classifier.^[64]

Variation in usage

A painting may be referred to with the classifiers 张 (張) zhāng and 幅 fú; both phrases have the same meaning, but convey different stylistic effects.^[65]

Depending on the classifier used, the noun 楼 lóu could be used to refer to either this building, as in 一座楼 (yí zuò lóu "one building"), or the floors of the building, as in 二十层楼 (èrshí céng lóu, "twenty floors").^[66]

It is not the case that every noun is only associated with one classifier. Across dialects and speakers there is great variability in the way classifiers are used for the same words, and speakers often do not agree which classifier is best.^[67] For example, for cars some people use 部 bù, others use 台 tái, and still others use 辆 (輛) liàng; Cantonese uses 架 gaa3. Even within a single dialect or a single speaker, the same noun may take different measure words depending on the style in which the person is speaking, or on different nuances the person wants to convey (for instance, measure words can reflect the speaker's judgment of or opinion about the object^[68]). An example of this is the word for person, 人 rén, which uses the measure word 个 (個) gè normally, but uses the measure 口 kǒu when counting number of people in a household, 位 wèi when being particularly polite or honorific, and 名 míng in formal, written contexts;^[69] likewise, a group of people may be referred to by massifiers as 一群人 (yì qún rén, "a group of people") or 一帮人 (yì bāng rén, "a gang/crowd of people"): the first is neutral, whereas the second implies that the people are unruly or otherwise being judged poorly.^[70]

Some count-classifiers may also be used with nouns that they are not normally related to, for metaphorical effect, as in 一堆烦恼 (yì duī fánnǎo, "a pile of worries/troubles").^[71] Finally, a single word may have multiple count-classifiers that convey different meanings altogether—in fact, the choice of a classifier can even influence the meaning of a noun. By way of illustration, 三节课 sān jié kè means "three class periods" (as in "I have three classes today"), whereas 三门课 sān mén kè means "three courses" (as in "I signed up for three courses this semester"), even though the noun in each sentence is the same.^[66]

Purpose

In research on classifier systems, and Chinese classifiers in particular, it has been asked why count-classifiers (as opposed to mass-classifiers) exist at all. Mass-classifiers are present in all languages since they are the only way to "count" mass nouns that are not naturally divided into units (as, for example, "three splotches of mud" in English; *"three muds" is ungrammatical). On the other hand, count-classifiers are not inherently mandatory, and are absent from most languages.^{[21][note 17]} Furthermore, count-classifiers are used with an "unexpectedly low frequency";^[72] in many settings, speakers avoid specific classifiers by just using a bare noun (without a number or demonstrative) or using the general classifier 个 gè.^[73] Linguists and typologists such as Joseph Greenberg have suggested that specific count-classifiers are semantically "redundant", repeating information present within the noun.^[74] Count-classifiers can be used stylistically, though,^[69] and can also be used to clarify or limit a speaker's intended meaning when using a vague or ambiguous noun; for example, the noun 课 kè "class" can refer to courses in a semester or specific class periods during a day, depending on whether the classifier 门 (門) mén or 节 (節) jié is used.^[75]

One proposed explanation for the existence of count-classifiers is that they serve more of a cognitive purpose than a practical one: in other words, they provide a linguistic way for speakers to organize or categorize real objects.^[76] An alternative account is that they serve more of a discursive and pragmatic function (a communicative function when people interact) rather than an abstract function within the mind.^[73] Specifically, it has been proposed that count-classifiers might be used to mark new or unfamiliar objects within a discourse,^[76] to introduce major characters or items in a story or conversation,^[77] or to foreground important information and objects by making them bigger and more salient.^[78] In this way, count-classifiers might not serve an abstract grammatical or cognitive function, but may help in communication by making important information more noticeable and drawing attention to it.

History

Classifier phrases

An oracle bone inscription from the Shāng Dynasty. Such inscriptions provide some of the earliest examples of the number phrases that may have eventually spawned Chinese classifiers.

Historical linguists have found that phrases consisting of nouns and numbers went through several structural changes in Old Chinese and Middle Chinese before classifiers appeared in them. The earliest forms may have been Number – Noun, like English (i.e. "five horses"), and the less common Noun – Number ("horses five"), both of which are attested in the oracle bone scripts of Pre-Archaic Chinese (circa 1400 BCE to 1000 BCE).^[79] The first constructions resembling classifier constructions were Noun – Number – Noun constructions, which were also extant in Pre-Archaic Chinese but less common than Number – Noun. In these constructions, sometimes the first and second nouns were identical (N1 – Number – N1, as in "horses five horses") and other times the second noun was different, but semantically related (N1 – Number – N2). According to some historical linguists, the N2 in these constructions can be considered an early form of count-classifier and has even been called an "echo classifier"; this speculation is not universally agreed on, though.^[80] Although true count-classifiers had not appeared yet, mass-classifiers were common in this time, with constructions such as "wine – six – yǒu" (the word 酉 yǒu represented a wine container) meaning "six yǒu of wine".^[80] Examples such as this suggest that mass-classifiers predate count-classifiers by several centuries, although they did not appear in the same word order as they do today.^[81]

It is from this type of structure that count-classifiers may have arisen, originally replacing the second noun (in structures where there was a noun rather than a mass-classifier) to yield Noun – Number – Classifier. That is to say, constructions like "horses five horses" may have been replaced by ones like "horses five CL", possibly for stylistic reasons such as avoiding repetition.^[82] Another reason for the appearance of count-classifiers may have been to avoid confusion or ambiguity that could have arisen from counting items using only mass-classifiers—i.e. to clarify when one is referring to a single item and when one is referring to a measure of items.^[83]

Historians agree that at some point in history the order of words in this construction shifted, putting the noun at the end rather than beginning, like in the present-day construction Number – Classifier – Noun.^[84] According to historical linguist Alain Peyraube, the earliest occurrences of this construction (albeit with mass-classifiers, rather than count-classifiers) appear in the late portion of Old Chinese (500 BCE to 200 BCE). At this time, the Number – Mass-classifier portion of the Noun – Number – Mass-classifier construction was sometimes shifted in front of the noun. Peyraube speculates that this may have occurred because it was gradually reanalyzed as a modifier (like an adjective) for the head noun, as opposed to a simple repetition as it originally was. Since Chinese generally places modifiers before modified, as does English, the shift may have been prompted by this reanalysis. By the early part of the Common Era, the nouns appearing in "classifier position" were beginning to lose their meaning and become true classifiers. Estimates of when classifiers underwent the most development vary: Wang Li claims their period of major development was during the Han Dynasty (206 BCE – 220 CE),^[85] whereas Liu Shiru estimates that it was the Southern and Northern Dynasties period (420 – 589 CE),^[86] and Peyraube chooses the Tang Dynasty (618 – 907 CE).^[87] Regardless of when they developed, Wang Lianqing claims that they did not become grammatically mandatory until sometime around the 11th century.^[88]

Classifier systems in many nearby languages and language groups (such as Vietnamese and the Tai languages) are very similar to the Chinese classifier system in both grammatical structure and the parameters along which some objects are grouped together. Thus, there has been some debate over which language family first developed classifiers and which ones then borrowed them—or whether classifier systems were native to all these languages and developed more through repeated language contact throughout history.^[89]

Classifier words

Most modern count-classifiers are derived from words that originally were free-standing nouns in older varieties of Chinese, and have since been grammaticalized to become bound morphemes.^[90] In other words, count-classifiers tend to come from words that once had specific meaning but lost it (a process known as semantic bleaching).^[91] Many, however, still have related forms that work as nouns all by themselves, such as the classifier 带 (帶) dài for long, ribbon-like objects: the modern word 带子 dàizi means "ribbon".^[71] In fact, the majority of classifiers can also be used as other parts of speech, such as nouns.^[92] Mass-classifiers, on the other hand, are more transparent in meaning than count-classifiers; while the latter have some historical meaning, the former are still full-fledged nouns. For example, 杯 (bēi, cup), is both a classifier as in 一杯茶 (yì bēi chá, "a cup of tea") and the word for a cup as in 酒杯 (jiǔbēi, "wine glass").^[93]

Where do these classifiers come from? Each classifier has its own history.

— Peyraube (1991, p. 116)

It was not always the case that every noun required a count-classifier. In many historical varieties of Chinese, use of classifiers was not mandatory, and classifiers are rare in writings that have survived.^[94] Some nouns acquired classifiers earlier than others; some of the first documented uses of classifiers were for inventorying items, both in mercantile business and in storytelling.^[95] Thus, the first nouns to have count-classifiers paired with them may have been nouns that represent "culturally valued" items such as horses, scrolls, and intellectuals.^[96] The special status of such items is still apparent today: many of the classifiers that can only be paired with one or two nouns, such as 匹 pǐ for horses^{[note 18]} and 首 shǒu for songs or poems, are the classifiers for these same "valued" items. Such classifiers make up as much as one-third of the commonly used classifiers today.^[19]

Classifiers did not gain official recognition as a lexical category (part of speech) until the 20th century. The earliest modern text to discuss classifiers and their use was Ma Jianzhong's 1898 Ma's Basic Principles for Writing Clearly (马氏文通).^[97] From then until the 1940s, linguists such as Ma, Wang Li, and Li Jinxi treated classifiers as just a type of noun that "expresses a quantity".^[85] Lü Shuxiang was the first to treat them as a separate category, calling them "unit words" (单位词 dānwèicí) in his 1940s Outline of Chinese Grammar (中国文法要略) and finally "measure words" (量词 liàngcí) in Grammar Studies (语法学习). He made this separation based on the fact that classifiers were semantically bleached, and that they can be used directly with a number, whereas true nouns need to have a measure word added before they can be used with a number.^[98] After this time, other names were also proposed for classifiers: Gao Mingkai called them "noun helper words" (助名词 zhùmíngcí), Lu Wangdao "counting markers" (计标 jìbiāo), and Japanese linguist Miyawaki Kennosuke called them "accompanying words" (陪伴词 péibàncí).^[99] In the Draft Plan for a System of Teaching Chinese Grammar [zh] adopted by the People's Republic of China in 1954, Lü's "measure words" (量词 liàngcí) was adopted as the official name for classifiers in China.^[100] This remains the most common term in use today.^[12]

General classifiers

Historically, 个 gè was not always the general classifier. Some believe it was originally a noun referring to bamboo stalks, and gradually expanded in use to become a classifier for many things with "vertical, individual, [or] upright qualit[ies]",^[101] eventually becoming a general classifier because it was used so frequently with common nouns.^[102] The classifier gè is actually associated with three different homophonous characters: 个, 個 (used today as the traditional-character equivalent of 个), and 箇. Historical linguist Lianqing Wang has argued that these characters actually originated from different words, and that only 箇 had the original meaning of "bamboo stalk".^[103] 个, he claims, was used as a general classifier early on, and may have been derived from the orthographically similar 介 jiè, one of the earliest general classifiers.^[104] 箇 later merged with 介 because they were similar in pronunciation and meaning (both used as general classifiers).^[103] Likewise, he claims that 個 was also a separate word (with a meaning having to do with "partiality" or "being a single part"), and merged with 个 for the same reasons as 箇 did; he also argues that 個 was "created", as early as the Han Dynasty, to supersede 个.^[105]

Nor was 个 the only general classifier in the history of Chinese. The aforementioned 介 jiè was being used as a general classifier before the Qin Dynasty (221 BCE); it was originally a noun referring to individual items out of a string of connected shells or clothes, and eventually came to be used as a classifier for "individual" objects (as opposed to pairs or groups of objects) before becoming a general classifier.^[106] Another general classifier was 枚 méi, which originally referred to small twigs. Since twigs were used for counting items, 枚 became a counter word: any items, including people, could be counted as "one 枚, two 枚", etc. 枚 was the most common classifier in use during the Southern and Northern Dynasties period (420–589 CE),^[107] but today is no longer a general classifier, and is only used rarely, as a specialized classifier for items such as pins and badges.^[108] Kathleen Ahrens has claimed that 隻 (zhī in Mandarin and jia in Taiwanese), the classifier for animals in Mandarin, is another general classifier in Taiwanese and may be becoming one in the Mandarin spoken in Taiwan.^[109]

Variety

Northern dialects tend to have fewer classifiers than southern ones. 個 ge is the only classifier found in the Dungan language. All nouns could have just one classifier in some dialects, such as Shanghainese (Wu), the Mandarin dialect of Shanxi, and Shandong dialects. Some dialects such as Northern Min, certain Xiang dialects, Hakka dialects, and some Yue dialects use 隻 for the noun referring to people, rather than 個.^[110]

See also

• China portal
• Languages portal

• List of Chinese classifiers
• Chinese grammar
• Collective noun
• Classifiers in other languages:
  • Burmese numerical classifiers
  • Hokkien counter word
  • Japanese counter word
  • Korean counter word
  • Vietnamese classifier

Notes

1. 
   

All examples given in this article are from standard Mandarin Chinese, with pronunciation indicated using the pinyin system, unless otherwise stated. The script would often be identical in other varieties of Chinese, although the pronunciation would vary.

Across different varieties of Chinese, classifier-noun clauses have slightly different interpretations (particularly in the interpretation of definiteness in classified nouns as opposed to bare nouns), but the requirement that a classifier come between a number and a noun is more or less the same in the major varieties (Cheng & Sybesma 2005).

Although “每” (每个人) is more generally used to mean "every person" in this case.

See, for example, similar results in the Chinese corpus of the Center for Chinese Linguistics at Peking University: 天空一片, retrieved on 3 June 2009.

In addition to the count-mass distinction and nominal-verbal distinction described below, various linguists have proposed many additional divisions of classifiers by type. He (2001, chapters 2 and 3) contains a review of these.

The Syllabus of Graded Words and Characters for Chinese Proficiency is a standardized measure of vocabulary and character recognition, used in the People's Republic of China for testing middle school students, high school students, and foreign learners. The most recent edition was published in 2003 by the Testing Center of the National Chinese Proficiency Testing Committee.

Including the following:

• Chen, Baocun 陈保存 (1988). Chinese Classifier Dictionary 汉语量词词典. Fuzhou: Fujian People's Publishing House 福建人民出版社. ISBN 978-7-211-00375-4.
• Fang, Jiqing; Connelly; Michael (2008). Chinese Measure Word Dictionary. Boston: Cheng & Tsui. ISBN 978-0-88727-632-3.
• Jiao, Fan 焦凡 (2001). A Chinese-English Dictionary of Measure Words 汉英量词词典. Beijing: Sinolingua 华语敎学出版社. ISBN 978-7-80052-568-1.
• Liu, Ziping 刘子平 (1996). Chinese Classifier Dictionary 汉语量词词典. Inner Mongolia Education Press 内蒙古教育出版社. ISBN 978-7-5311-2707-9.

Count-classifiers have also been called "individual classifiers", (Chao 1968, p. 509), "qualifying classifiers" (Zhang 2007, p. 45; Hu 1993, p. 10), and just "classifiers" (Cheng & Sybesma 1998, p. 3).

Mass-classifiers have also been called "measure words", "massifiers" (Cheng & Sybesma 1998, p. 3), "non-individual classifiers" (Chao 1968, p. 509), and "quantifying classifiers" (Zhang 2007, p. 45; Hu 1993, p. 10). The term "mass-classifier" is used in this article to avoid ambiguous usage of the term "measure word", which is often used in everyday speech to refer to both count-classifiers and mass-classifiers, even though in technical usage it only means mass-classifiers (Li 2000, p. 1116).

Also called "aggregate" (Li & Thompson 1981, pp. 107–109) or "group" (Ahrens 1994, p. 239, note 3) measures.

"Classifier phrases" are similar to noun phrases, but with a classifier rather than a noun as the head (Cheng & Sybesma 1998, pp. 16–17).

This may be because official documents during the Han Dynasty were written on long bamboo strips, making them "strips of business" (Ahrens 1994, p. 206).

The theory described in Ahrens (1994) and Wang (1994) is also referred to within those works as a "prototype" theory, but differs somewhat from the version of prototype theory described here; rather than claiming that individual prototypes are the source for classifier meanings, these authors believe that classifiers still are based on categories with features, but that the categories have many features, and "prototypes" are words that have all the features of that category whereas other words in the category only have some features. In other words, "there are core and marginal members of a category.... a member of a category does not necessarily possess all the properties of that category" (Wang 1994, p. 8). For instance, the classifier 棵 kē is used for the category of trees, which may have features such as "has a trunk", "has leaves", and "has branches", "is deciduous"; maple trees would be prototypes of the category, since they have all these features, whereas palm trees only have a trunk and leaves and thus are not prototypical (Ahrens 1994, pp. 211–12).

The apparent disagreement between the definitions provided by different authors may reflect different uses of these words in different time periods. It is well-attested that many classifiers underwent frequent changes of meaning throughout history (Wang 1994; Erbaugh 1986, pp. 426–31; Ahrens 1994, pp. 205–206), so 匹 pǐ may have had all these meanings at different points in history.

Also called "sortal classifiers" (Erbaugh 2000, p. 33; Biq 2002, p. 531).

Kathleen Ahrens claimed in 1994 that the classifier for animals—只 (隻), pronounced zhī in Mandarin and jia in Taiwanese—is in the process of becoming a second general classifier in the Mandarin spoken in Taiwan, and already is used as the general classifier in Taiwanese itself (Ahrens 1994, p. 206).

Although English does not have a productive system of count-classifiers and is not considered a "classifier language", it does have a few constructions—mostly archaic or specialized—that resemble count-classifiers, such as "X head of cattle" (T'sou 1976, p. 1221).

18. Today, 匹 may also be used for bolts of cloth. See "List of Common Nominal Measure Words" on ChineseNotes.com (last modified 11 January 2009; retrieved on 3 September 2009).

References

1. 
   

Li & Thompson 1981, p. 104

Hu 1993, p. 13

The examples are adapted from those given in Hu (1993, p. 13), Erbaugh (1986, pp. 403–404), and Li & Thompson (1981, pp. 104–105).

Zhang 2007, p. 47

Li 2000, p. 1119

Sun 2006, p. 159

Sun 2006, p. 160

Li & Thompson 1981, p. 82

Li & Thompson 1981, pp. 34–35

Li & Thompson 1981, p. 111

Hu 1993, p. 9

Li 2000, p. 1116; Hu 1993, p. 7; Wang 1994, pp. 22, 24–25; He 2001, p. 8. Also see the usage in Fang & Connelly (2008) and most introductory Chinese textbooks.

Li & Thompson 1981, p. 105

Chao 1968, section 7.9

Zhang 2007, p. 44

Erbaugh 1986, p. 403; Fang & Connelly 2008, p. ix

He 2001, p. 234

Gao & Malt 2009, p. 1133

Erbaugh 1986, p. 403

Erbaugh 1986, p. 404

Tai 1994, p. 3; Allan 1977, pp. 285–86; Wang 1994, p. 1

Ahrens 1994, p. 239, note 3

Li & Thompson 1981, p. 105; Zhang 2007, p. 44; Erbaugh 1986, p. 118, note 5

Li & Thompson 1981, pp. 105–107

Erbaugh 1986, p. 118, note 5; Hu 1993, p. 9

Erbaugh 1986, p. 118, note 5; Li & Thompson 1981, pp. 107–109

Cheng & Sybesma 1998, p. 3; Tai 1994, p. 2

Wang 1994, pp. 27–36; Cheng & Sybesma 1998

Cheng & Sybesma 1998, pp. 3–5

Wang 1994, pp. 29–30

Cheng & Sybesma 1998

Ahrens 1994, p. 239, note 5; Wang 1994, pp. 26–27, 37–48

He 2001, pp. 42, 44

Zhang 2007, p. 44; Li & Thompson 1981, p. 110; Fang & Connelly 2008, p. x

Tai 1994, p. 8

Tai 1994, pp. 7–9; Tai & Wang 1990

Erbaugh 1986, p. 111

He 2001, p. 239

Tai 1994, pp. 3–5; Ahrens 1994, pp. 208–12

Tai 1994, p. 3; Ahrens 1994, pp. 209–10

Tai 1994, p. 5; Allan 1977

Hu 1993, p. 1

Tai 1994, p. 12

Zhang 2007, pp. 46–47

Erbaugh 1986, p. 415

Hu 1993, p. 1; Tai 1994, p. 13; Zhang 2007, pp. 55–56

Zhang 2007, pp. 55–56

Gao & Malt 2009, p. 1134

Morev 2000, p. 79

Wang 1994, pp. 172–73

Tai 1994, p. 15, note 7

Tai 1994, p. 13

Gao & Malt 2009, pp. 1133–4

Hu 1993, p. 12

Tzeng, Chen & Hung 1991, p. 193

Zhang 2007, p. 57

Ahrens 1994, p. 212

He 2001, p. 165

Erbaugh 1986; Hu 1993

Ahrens 1994, pp. 227–32

Tzeng, Chen & Hung 1991

Erbaugh 1986, pp. 404–406; Ahrens 1994, pp. 202–203

Erbaugh 1986, pp. 404–406

Ahrens 1994

Zhang 2007, p. 53

Zhang 2007, p. 52

Tai 1994; Erbaugh 2000, pp. 34–35

He 2001, p. 237

Fang & Connelly 2008, p. ix; Zhang 2007, pp. 53–54

He 2001, p. 242

Shie 2003, p. 76

Erbaugh 2000, p. 34

Erbaugh 2000, pp. 425–26; Li 2000

Zhang 2007, p. 51

Zhang 2007, pp. 51–52

Erbaugh 1986, pp. 425–6

Sun 1988, p. 298

Li 2000

Peyraube 1991, p. 107; Morev 2000, pp. 78–79

Peyraube 1991, p. 108

Peyraube 1991, p. 110; Wang 1994, pp. 171–72

Morev 2000, pp. 78–79

Wang 1994, p. 172

Peyraube 1991, p. 106; Morev 2000, pp. 78–79

He 2001, p. 3

Wang 1994, pp. 2, 17

Peyraube 1991, pp. 111–17

Wang 1994, p. 3

Erbaugh 1986, p. 401; Wang 1994, p. 2

Shie 2003, p. 76; Wang 1994, pp. 113–14, 172–73

Peyraube 1991, p. 116

Gao & Malt 2009, p. 1130

Chien, Lust & Chiang 2003, p. 92

Peyraube 1991; Erbaugh 1986, p. 401

Erbaugh 1986, p. 401

Erbaugh 1986, pp. 401, 403, 428

He 2001, p. 2

He 2001, p. 4

He 2001, pp. 5–6

He 2001, p. 7

Erbaugh 1986, p. 430

Erbaugh 1986, pp. 428–30; Ahrens 1994, p. 205

Wang 1994, pp. 114–15

Wang 1994, p. 95

Wang 1994, pp. 115–16, 158

Wang 1994, pp. 93–95

Wang 1994, pp. 155–7

Erbaugh 1986, p. 428

Ahrens 1994, p. 206

110. Graham Thurgood; Randy J. LaPolla (2003). Graham Thurgood, Randy J. LaPolla (ed.). The Sino-Tibetan languages. Routledge language family. Vol. 3 (illustrated ed.). Psychology Press. p. 85. ISBN 0-7007-1129-5. Retrieved 2012-03-10. In general, the Southern dialects have a greater number of classifiers than the Northern. The farther north one travels, the smaller the variety of classifiers found. In Dunganese, a Gansu dialect of Northern Chinese spoken in Central Asia, only one classifier, 個 [kə], is used; and this same classifier has almost become the cover classifier for all nouns in Lánzhou of Gansu too. The tendency to use one general classifier for all nouns is also found to a greater or lesser extent in many Shanxi dialects, some Shandong dialects, and even the Shanghai dialect of Wu and Standard Mandarin (SM). The choice of classifiers for individual nouns is particular to each dialect. For example, although the preferred classifier across dialects for 'human being' is 個 and its cognates, 隻 in its dialect forms is widely used in the Hakka and Yue dialects of Guangxi and western Guangdong provinces as well as in the Northern Min dialects and some Xiang dialects in Hunan.

Bibliography

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• Allan, Keith (1977). "Classifiers". Language. Linguistic Society of America. 53 (2): 285–311. doi:10.2307/413103. JSTOR 413103.
• Biq, Yung-O (2002). "Classifier and construction: the interaction of grammatical categories and cognitive strategies" (PDF). Language and Linguistics. 3 (3): 521–42. Archived from the original (PDF) on 2019-07-11.
• Chao, Yuen Ren (1968). A Grammar of Spoken Chinese. Berkeley: University of California Press.
• Cheng, Lisa L.-S.; Sybesma, Rint (1998). "yi-wan tang and yi-ge Tang: Classifiers and mass-classifiers". Tsing Hua Journal of Chinese Studies. 28 (3).
• Cheng, Lisa L.-S.; Sybesma, Rint (2005). "Classifiers in four varieties of Chinese". In Cinque, Guglielmo; Kayne, Richard S. (eds.). The Oxford Handbook of Comparative Syntax. Oxford University Press. ISBN 0-19-513650-0.
• Chien, Yu-Chin; Lust, Barbara; Chiang, Chi-Pang (2003). "Chinese children's comprehension of count-classifiers and mass-classifiers". Journal of East Asian Linguistics. 12 (2): 91–120. doi:10.1023/A:1022401006521.
• Erbaugh, Mary S. (1986). "Taking stock: the development of Chinese noun classifiers historically and in young children". In Colette Craig (ed.). Noun classes and categorization. J. Benjamins. pp. 399–436. ISBN 978-0-915027-33-0.
• Erbaugh, Mary S. (2000). Classifiers are for specification: complementary functions for sortal and general classifiers in Cantonese and Mandarin. 33rd International Conference on Sino-Tibetan Languages and Linguistics.
• Fang, Jiqing; Connelly, Michael (2008). Chinese Measure Word Dictionary. Boston: Cheng & Tsui. ISBN 978-0-88727-632-3.
• Gao, Ming; Malt, Barbara (2009). "Mental representation and cognitive consequences of Chinese individual classifiers". Language and Cognitive Processes. 24 (7/8): 1124–1179. doi:10.1080/01690960802018323.
• He, Jie (何杰) (2001). Studies on classifiers in Modern Chinese (现代汉语量词研究) (in Chinese) (2nd ed.). Beijing: Nationalities Publishing House (民族出版社). ISBN 978-7-105-04714-7.
• Hu, Qian (1993). The acquisition of Chinese classifiers by young Mandarin-speaking children (Ph.D. dissertation). Boston University.
• Li, Charles N.; Thompson, Sandra A. (1981). Mandarin Chinese: A Functional Reference Grammar. Los Angeles: University of California Press. ISBN 978-0-520-06610-6.
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• Morev, Lev (2000). "Some afterthoughts on classifiers in the Tai languages" (PDF). The Mon-Khmer Studies Journal. 30: 75–82.
• Peyraube, Alain (1991). "Some remarks on the history of Chinese classifiers". In Clancy, Patricia Marie; Thompson, Sandra A. (eds.). Asian Discourse and Grammar. Linguistics. Vol. 3. pp. 106–126.
• Shie, Jian-Shiung (2003). "Figurative Extension of Chinese Classifiers" (PDF). Journal of Da-Yeh University. 12 (2): 73–83.
• Sun, Chaofen (1988). "The discourse function of numeral classifiers in Mandarin Chinese". Journal of Chinese Linguistics. 2 (2): 298–322. JSTOR 23757862.
• Sun, Chaofen (2006). Chinese: A Linguistic Introduction. Cambridge University Press. ISBN 978-0-521-82380-7.
• T'sou, Benjamin K. (1976). "The structure of nominal classifier systems" (PDF). Oceanic Linguistics Special Publications, number 13. Austroasiatic Studies Part II. University of Hawai'i Press. pp. 1215–1247.
• Tai, James H.-Y. (1994). "Chinese classifier systems and human categorization". In Wang, Willian S.-Y.; Chen, M. Y.; Tzeng, Ovid J.L. (eds.). In honor of William S.-Y. Wang: Interdisciplinary studies on language and language change. Taipei: Pyramid Press. pp. 479–494. ISBN 978-957-9268-55-4.
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External links

• List of Common Nominal Measure Words on chinesenotes.com
• Units of Weights and Measures on chinesenotes.com
• How to Use Chinese Measure Words on 3000 Hanzi

v t e Chinese language or Sinitic languages

Categories:

• Chinese grammar
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https://en.wikipedia.org/wiki/Chinese_classifier#Count-classifiers_and_mass-classifiers

 

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Single-crystalline GeTe nanowires and nanohelices

Semiconducting GeTe nanowires (NW) and nanohelices (NH) are synthesized via vapor transport method, with metal nanoparticle catalysts. GeTe was evaporated and carried by Ar gas at optimum temperature, pressure, time, and gas flow rate to the downstream collecting/grow site (SiO₂ surface coated with colloidal gold nanoparticles). High temperature over 500 °C produces thicker nanowires and crystalline chunks. Au is essential to the growth of NW and NH and is suggested to the metal catalyst of the reaction. This method gives rise to NW and NH with a 1:1 ratio of Ge and Te. NW produced by this method average about 65 nm in diameter and up to 50 μm in length. NHs averages to 135 nm in helix diameter.^[9]

Nanocrystal (quantum size effect)

The synthesis described above has not reached the sized required to exhibit quantum size effect. Nanostructures that reach the quantum regime exhibit a different set of phenomena unseen at a larger scale, for example, spontaneous polar ordering and the splitting of diffraction spots. The synthesis of GeTe nanocrystals of average size of 8, 17, and 100 nm involves divalent Ge(II) chloride – 1,4 dioxane complex and bis[bis(trimethylsilyl)amino]Ge (II) and trioctylphosphine-tellurium in a solvent such as 1,2-dichlorobenzene or phenyl ether. Ge(II) reduction kinetics has been thought to determine the GeTe formation. Large the Ge(II) reduction rate may lead to the increase in particle nucleation rate, resulting in the reduction of particle diameter.^[10] 

https://en.wikipedia.org/wiki/Germanium_telluride#Single-crystalline_GeTe_nanowires_and_nanohelices

 

"Hymn to the Fallen" (Jiu Ge) (traditional Chinese: 國殤; simplified Chinese: 国殇; pinyin: Guó shāng; lit. 'National casualties') is a Classical Chinese poem which has been preserved in the Nine Songs (Jiu Ge) section of the ancient Chinese poetry anthology, the Chu ci, or The Songs of Chu, which is an ancient set of poems. Together, these poems constitute one of the 17 sections of the poetry anthology which was published under the title of the Chuci (also known as the Songs of Chu or as the Songs of the South). Despite the "Nine" in the title (Jiu ge literally means Nine Songs), the number of these poetic pieces actually consists of eleven separate songs, or elegies.^[1] This set of verses seems to represent some shamanistic dramatic practices of the Yangzi River valley area (as well as a northern tradition or traditions) involving the invocation of divine beings and seeking their blessings by means of a process of courtship.^[2] The poetry consists of lyrics written for performance as part of a religious drama, however the lack of stage directions or indications of who is supposed to be singing at any one time or whether some of the lines represent lines for a chorus makes an accurate reconstruction of how such a shamanic drama would actually have been performed quite uncertain; although, there are internal textual clues, for example indicating the use of spectacular costumes for the performers, and an extensive orchestra.^[3] Although not precisely dated, "Hymn to the Fallen" dates from the end of the late the Warring States period, ended 221 BCE, with possible revisions in the Han dynasty, particularly during the reign of Han Wudi, during 141 to 87 BCE . The poem has been translated into English by David Hawkes as "Hymn to the Fallen". "Guo shang" is a hymn to soldiers killed in war. Guó (國) means the "state", "kingdom", or "nation". Shāng (殤) means to "die young". Put together, the title refers to those who meet death in the course of fighting for their country. David Hawkes describes it as "surely one of the most beautiful laments for fallen soldiers in any language".^[4] 

https://en.wikipedia.org/wiki/Hymn_to_the_Fallen_(Jiu_Ge)

 

 

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In computer architecture, registers are typically addressed by mechanisms other than main memory, but may in some cases be assigned a memory address e.g. DEC PDP-10, ICT 1900.[2] Almost all computers, whether load/store architecture or not, load items of data from a larger memory into registers where they are used for arithmetic operations, bitwise operations, and other operations, and are manipulated or tested by machine instructions. Manipulated items are then often stored back to main memory, either by the same instruction or by a subsequent one. Modern processors use either static or dynamic RAM as main memory, with the latter usually accessed via one or more cache levels. Processor registers are normally at the top of the memory hierarchy, and provide the fastest way to access data. The term normally refers only to the group of registers that are directly encoded as part of an instruction, as defined by the instruction set. 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In some instruction sets, the registers can operate in various modes, breaking down their storage memory into smaller parts (32-bit into four 8-bit ones, for instance) to which multiple data (vector, or one-dimensional array of data) can be loaded and operated upon at the same time. Typically it is implemented by adding extra registers that map their memory into a larger register. Processors that have the ability to execute single instructions on multiple data are called vector processors. https://en.wikipedia.org/wiki/Processor_register A geolocation-based video game or location-based video game is a type of video game where the gameplay evolves and progresses via a player's location in the world, often attained using GPS. Most location-based video games are mobile games that make use of the mobile phone's built in GPS capability, and often have real-world map integration. One of the most recognizable location-based mobile games is Pokémon Go. Location-based (GPS) games are often conflated with augmented reality (AR) games. GPS and AR are two separate technologies which are sometimes both used in a game, like in Pokémon Go and Minecraft Earth. GPS and AR functionality largely do not depend on one another but are often used in concert. A video game may be an AR game, a location-based game, both, or neither. https://en.wikipedia.org/wiki/Geolocation-based_video_game https://en.wikipedia.org/wiki/Augmented_reality https://en.wikipedia.org/wiki/Alternate_reality https://en.wikipedia.org/wiki/Multiverse https://en.wikipedia.org/wiki/Virtual_reality https://en.wikipedia.org/wiki/Simulation_hypothesis https://en.wikipedia.org/wiki/Realization_(probability) https://en.wikipedia.org/wiki/Empirical_probability Realization is the art of creating music, typically an accompaniment, from a figured bass, whether by improvisation in real time, or as a detained exercise in writing. It is most commonly associated with Baroque music. https://en.wikipedia.org/wiki/Realization_(figured_bass) Realization, also called Biographie, is a circa 35-metre (115 ft) sport climbing route on a limestone cliff on the southern face of Céüse mountain, near Gap and Sigoyer, in France. After it was first climbed in 2001 by American climber Chris Sharma, it became the first rock climb in the world to have a consensus grade of 9a+ (5.15a).[a] It is considered an historic and important route in rock climbing, and one of the most attempted climbs at its grade.[5][6] https://en.wikipedia.org/wiki/Realization_(climb) In metrology, the realisation of a unit of measure is the conversion of its definition into reality.[1] The International vocabulary of metrology identifies three distinct methods of realisation: Realisation of a measurement unit from its definition. Reproduction of measurement standards. Adopting a particular artefact as a standard. The International Bureau of Weights and Measures maintains the techniques for realisation of the base units in the International System of Units (SI).[2] https://en.wikipedia.org/wiki/Realisation_(metrology) Realized niche width is a phrase relating to ecology, is defined by the actual space that an organism inhabits and the resources it can access as a result of limiting pressures from other species (e.g. superior competitors). An organism's ecological niche is determined by the biotic and abiotic factors that make up that specific ecosystem that allow that specific organism to survive there. The width of an organism's niche is set by the range of conditions a species is able to survive in that specific environment. https://en.wikipedia.org/wiki/Realized_niche_width Realizing Increased Photosynthetic Efficiency (RIPE) is a translational research project that is genetically engineering plants to photosynthesize more efficiently to increase crop yields.[1] RIPE aims to increase agricultural production worldwide, particularly to help reduce hunger and poverty in Sub-Saharan Africa and Southeast Asia by sustainably improving the yield of key food crops including soybeans, rice, cassava[2] and cowpeas.[3] The RIPE project began in 2012, funded by a five-year, $25-million dollar grant from the Bill and Melinda Gates Foundation.[4] In 2017, the project received a $45 million-dollar reinvestment from the Gates Foundation, Foundation for Food and Agriculture Research, and the UK Government's Department for International Development.[5] In 2018, the Gates Foundation contributed an additional $13 million to accelerate the project's progress.[6] https://en.wikipedia.org/wiki/Realizing_Increased_Photosynthetic_Efficiency Realized variance or realised variance (RV, see spelling differences) is the sum of squared returns. For instance the RV can be the sum of squared daily returns for a particular month, which would yield a measure of price variation over this month. More commonly, the realized variance is computed as the sum of squared intraday returns for a particular day. The realized variance is useful because it provides a relatively accurate measure of volatility[1] which is useful for many purposes, including volatility forecasting and forecast evaluation. https://en.wikipedia.org/wiki/Realized_variance The Age of Enlightenment or the Enlightenment,[note 2] also known as the Age of Reason, was an intellectual and philosophical movement that occurred in Europe in the 17th and 18th centuries, with global influences and effects.[2][3] The Enlightenment included a range of ideas centered on the value of human happiness, the pursuit of knowledge obtained by means of reason and the evidence of the senses, and ideals such as natural law, liberty, progress, toleration, fraternity, constitutional government, and separation of church and state.[4][5] https://en.wikipedia.org/wiki/Age_of_Enlightenment https://en.wikipedia.org/wiki/Knowledge Definitions of knowledge try to determine the essential features of knowledge. Closely related terms are conception of knowledge, theory of knowledge, and analysis of knowledge. Some general features of knowledge are widely accepted among philosophers, for example, that it constitutes a cognitive success or an epistemic contact with reality and that propositional knowledge involves true belief. Most definitions of knowledge in analytic philosophy focus on propositional knowledge or knowledge-that, as in knowing that Dave is at home, in contrast to knowledge-how (know-how) expressing practical competence. However, despite the intense study of knowledge in epistemology, the disagreements about its precise nature are still both numerous and deep. Some of those disagreements arise from the fact that different theorists have different goals in mind: some try to provide a practically useful definition by delineating its most salient feature or features, while others aim at a theoretically precise definition of its necessary and sufficient conditions. Further disputes are caused by methodological differences: some theorists start from abstract and general intuitions or hypotheses, others from concrete and specific cases, and still others from linguistic usage. Additional disagreements arise concerning the standards of knowledge: whether knowledge is something rare that demands very high standards, like infallibility, or whether it is something common that requires only the possession of some evidence. One definition that many philosophers consider to be standard, and that has been discussed since ancient Greek philosophy, is justified true belief (JTB). This implies that knowledge is a mental state and that it is not possible to know something false. There is widespread agreement among analytic philosophers that knowledge is a form of true belief. The idea that justification is an additionally required component is due to the intuition that true beliefs based on superstition, lucky guesses, or erroneous reasoning do not constitute knowledge. In this regard, knowledge is more than just being right about something. The source of most disagreements regarding the nature of knowledge concerns what more is needed. According to the standard philosophical definition, it is justification. The original account understands justification internalistically as another mental state of the person, like a perceptual experience, a memory, or a second belief. This additional mental state supports the known proposition and constitutes a reason or evidence for it. However, some modern versions of the standard philosophical definition use an externalistic conception of justification instead. Many such views affirm that a belief is justified if it was produced in the right way, for example, by a reliable cognitive process. The justified-true-belief definition of knowledge came under severe criticism in the second half of the 20th century, mainly due to a series of counterexamples given by Edmund Gettier. Most of these examples aim to illustrate cases in which a justified true belief does not amount to knowledge because its justification is not relevant to its truth. This is often termed epistemic luck since it is just a fortuitous coincidence that the justified belief is also true. A few epistemologists have concluded from these counterexamples that the JTB definition of knowledge is deeply flawed and have sought a radical reconception of knowledge. However, many theorists still agree that the JTB definition is on the right track and have proposed more moderate responses to deal with the suggested counterexamples. Some hold that modifying one's conception of justification is sufficient to avoid them. Another approach is to include an additional requirement besides justification. On this view, being a justified true belief is a necessary but not a sufficient condition of knowledge. A great variety of such criteria has been suggested. They usually manage to avoid many of the known counterexamples but they often fall prey to newly proposed cases. It has been argued that, in order to circumvent all Gettier cases, the additional criterion needs to exclude epistemic luck altogether. However, this may require the stipulation of a very high standard of knowledge: that nothing less than infallibility is needed to exclude all forms of luck. The defeasibility theory of knowledge is one example of a definition based on a fourth criterion besides justified true belief. The additional requirement is that there is no truth that would constitute a defeating reason of the belief if the person knew about it. Other alternatives to the JTB definition are reliabilism, which holds that knowledge has to be produced by reliable processes, causal theories, which require that the known fact caused the knowledge, and virtue theories, which identify knowledge with the manifestation of intellectual virtues. Not all forms of knowledge are propositional, and various definitions of different forms of non-propositional knowledge have also been proposed. But among analytic philosophers this field of inquiry is less active and characterized by less controversy. Someone has practical knowledge or know-how if they possess the corresponding competence or ability. Knowledge by acquaintance constitutes a relation not to a proposition but to an object. It is defined as familiarity with its object based on direct perceptual experience of it. https://en.wikipedia.org/wiki/Definitions_of_knowledge Knowledge transfer is the sharing or disseminating of knowledge and the providing of inputs to problem solving.[1] In organizational theory, knowledge transfer is the practical problem of transferring knowledge from one part of the organization to another. Like knowledge management, knowledge transfer seeks to organize, create, capture or distribute knowledge and ensure its availability for future users. It is considered to be more than just a communication problem. If it were merely that, then a memorandum, an e-mail or a meeting would accomplish the knowledge transfer. Knowledge transfer is more complex because: knowledge resides in organizational members, tools, tasks, and their subnetworks[2] and much knowledge in organizations is tacit or hard to articulate.[3] The subject has been taken up under the title of knowledge management since the 1990s. The term has also been applied to the transfer of knowledge at the international level.[4][5] In business, knowledge transfer now has become a common topic in mergers and acquisitions.[6] It focuses on transferring technological platform, market experience, managerial expertise, corporate culture, and other intellectual capital that can improve the companies' competence.[7] Since technical skills and knowledge are very important assets for firms' competence in the global competition,[8] unsuccessful knowledge transfer can have a negative impact on corporations and lead to the expensive and time-consuming M&A not creating values to the firms.[9] https://en.wikipedia.org/wiki/Knowledge_transfer Knowledge extraction is the creation of knowledge from structured (relational databases, XML) and unstructured (text, documents, images) sources. The resulting knowledge needs to be in a machine-readable and machine-interpretable format and must represent knowledge in a manner that facilitates inferencing. Although it is methodically similar to information extraction (NLP) and ETL (data warehouse), the main criterion is that the extraction result goes beyond the creation of structured information or the transformation into a relational schema. It requires either the reuse of existing formal knowledge (reusing identifiers or ontologies) or the generation of a schema based on the source data. The RDB2RDF W3C group [1] is currently standardizing a language for extraction of resource description frameworks (RDF) from relational databases. Another popular example for knowledge extraction is the transformation of Wikipedia into structured data and also the mapping to existing knowledge (see DBpedia and Freebase). https://en.wikipedia.org/wiki/Knowledge_extraction In philosophy, a distinction is often made between two different kinds of knowledge: knowledge by acquaintance and knowledge by description. Whereas knowledge by description is something like ordinary propositional knowledge (e.g. "I know that snow is white"), knowledge by acquaintance is familiarity with a person, place, or thing, typically obtained through perceptual experience (e.g. "I know Sam", "I know the city of Bogotá", or "I know Russell's Problems of Philosophy").[1] According to Bertrand Russell's classic account of acquaintance knowledge, acquaintance is a direct causal interaction between a person and some object that the person is perceiving. https://en.wikipedia.org/wiki/Knowledge_by_acquaintance The knowledge economy (or the knowledge-based economy) is an economic system in which the production of goods and services is based principally on knowledge-intensive activities that contribute to advancement in technical and scientific innovation.[1] The key element of value is the greater dependence on human capital and intellectual property for the source of the innovative ideas, information and practices.[2] Organisations are required to capitalise this "knowledge" into their production to stimulate and deepen the business development process. There is less reliance on physical input and natural resources. A knowledge-based economy relies on the crucial role of intangible assets within the organisations' settings in facilitating modern economic growth.[3] https://en.wikipedia.org/wiki/Knowledge_economy The knowledge argument (also known as Mary's Room or Mary the super-scientist) is a philosophical thought experiment proposed by Frank Jackson in his article "Epiphenomenal Qualia" (1982) and extended in "What Mary Didn't Know" (1986). The experiment describes Mary, a scientist who exists in a black-and-white world where she has extensive access to physical descriptions of color, but no actual perceptual experience of color. Mary has learned everything there is to learn about color, but she has never actually experienced it for herself. The central question of the thought experiment is whether Mary will gain new knowledge when she goes outside the colorless world and experiences seeing in color https://en.wikipedia.org/wiki/Knowledge_argument Knowledge management (KM) is the collection of methods relating to creating, sharing, using and managing the knowledge and information of an organization.[1] It refers to a multidisciplinary approach to achieve organizational objectives by making the best use of knowledge.[2] https://en.wikipedia.org/wiki/Knowledge_management Embedding of a knowledge graph. The vector representation of the entities and relations can be used for different machine learning applications. In representation learning, knowledge graph embedding (KGE), also referred to as knowledge representation learning (KRL), or multi-relation learning,[1] is a machine learning task of learning a low-dimensional representation of a knowledge graph's entities and relations while preserving their semantic meaning.[1][2][3] Leveraging their embedded representation, knowledge graphs (KGs) can be used for various applications such as link prediction, triple classification, entity recognition, clustering, and relation extraction.[1][4] https://en.wikipedia.org/wiki/Knowledge_graph_embedding A relationship extraction task requires the detection and classification of semantic relationship mentions within a set of artifacts, typically from text or XML documents. The task is very similar to that of information extraction (IE), but IE additionally requires the removal of repeated relations (disambiguation) and generally refers to the extraction of many different relationships. https://en.wikipedia.org/wiki/Relationship_extraction A document is a written, drawn, presented, or memorialized representation of thought, often the manifestation of non-fictional, as well as fictional, content. The word originates from the Latin Documentum, which denotes a "teaching" or "lesson": the verb doceō denotes "to teach". In the past, the word was usually used to denote written proof useful as evidence of a truth or fact. In the Computer Age, "document" usually denotes a primarily textual computer file, including its structure and format, e.g. fonts, colors, and images. Contemporarily, "document" is not defined by its transmission medium, e.g., paper, given the existence of electronic documents. "Documentation" is distinct because it has more denotations than "document". Documents are also distinguished from "realia", which are three-dimensional objects that would otherwise satisfy the definition of "document" because they memorialize or represent thought; documents are considered more as 2-dimensional representations. While documents can have large varieties of customization, all documents can be shared freely and have the right to do so, creativity can be represented by documents, also. History, events, examples, opinions, etc. all can be expressed in documents. https://en.wikipedia.org/wiki/Document In library classification systems, realia are three-dimensional objects from real life such as coins, tools, and textiles, that do not fit into the traditional categories of library material. They can be either man-made (artifacts, tools, utensils, etc.) or naturally occurring (specimens, samples, etc.), usually borrowed, purchased, or received as donation by a teacher, library, or museum for use in classroom instruction or in exhibits. Archival and manuscript collections often receive items of memorabilia such as badges, emblems, insignias, jewelry, leather goods, needlework, etc., in connection with gifts of personal papers. Most government or institutional archives reject gifts of non-documentary objects unless they have a documentary value. When accepting large bequests of mixed objects they normally have the donors sign legal documents giving permission to the archive to destroy, exchange, sell, or dispose in any way those objects which, according to the best judgement of the archivist, are not manuscripts (which can include typescripts or printouts) or are not immediately useful for understanding the manuscripts. Recently, the usage of this term has been criticized by librarians based on the usage of term realia to refer to artistic and historical artifacts and objects, and suggesting the use of the phrase "real world object" to describe the broader categories of three-dimensional objects in libraries. https://en.wikipedia.org/wiki/Realia_(library_science) https://en.wikipedia.org/wiki/Knowledge_Web https://en.wikipedia.org/wiki/Commonsense_knowledge_(artificial_intelligence) https://en.wikipedia.org/wiki/Zero_knowledge https://en.wikipedia.org/wiki/Knowledge_Network https://en.wikipedia.org/wiki/Tacit_knowledge https://en.wikipedia.org/wiki/Procedural_knowledge https://en.wikipedia.org/wiki/The_Archaeology_of_Knowledge https://en.wikipedia.org/wiki/Knowledge_distillation https://en.wikipedia.org/wiki/Definitions_of_knowledge https://en.wikipedia.org/wiki/Knowledge_representation_and_reasoning https://en.wikipedia.org/wiki/Divine_knowledge https://en.wikipedia.org/wiki/Curse_of_knowledge https://en.wikipedia.org/wiki/Decolonization_of_knowledge https://en.wikipedia.org/wiki/Science https://en.wikipedia.org/wiki/Word_of_Knowledge https://en.wikipedia.org/wiki/Knowledge_base https://en.wikipedia.org/wiki/Encyclopedia https://en.wikipedia.org/wiki/Desacralization_of_knowledge https://en.wikipedia.org/wiki/Meta-knowledge https://en.wikipedia.org/wiki/Metacognition#Metastrategic_knowledge https://en.wikipedia.org/wiki/Core_Knowledge_Foundation https://en.wikipedia.org/wiki/Western_esotericism https://en.wikipedia.org/wiki/Dangerous_Knowledge https://en.wikipedia.org/wiki/Coloniality_of_knowledge https://en.wikipedia.org/wiki/Gettier_problem https://en.wikipedia.org/wiki/Artificial_intelligence#Knowledge_representation https://en.wikipedia.org/wiki/Ontology_language#Classification_of_ontology_languages https://en.wikipedia.org/wiki/Academic_discipline https://en.wikipedia.org/wiki/Forbidden_fruit https://en.wikipedia.org/wiki/Knowledge,_Skills,_and_Abilities https://en.wikipedia.org/wiki/Knowledge_Navigator https://en.wikipedia.org/wiki/Knowledge_and_Its_Limits https://en.wikipedia.org/wiki/Monopolies_of_knowledge https://en.wikipedia.org/wiki/Knowledge_(legal_construct) https://en.wikipedia.org/wiki/Empirical_evidence https://en.wikipedia.org/wiki/Self-knowledge https://en.wikipedia.org/wiki/Tree_of_the_knowledge_of_good_and_evil https://en.wikipedia.org/wiki/Knowledge_acquisition https://en.wikipedia.org/wiki/Open_knowledge https://en.wikipedia.org/wiki/Book_of_Knowledge https://en.wikipedia.org/wiki/Taxes_on_knowledge https://en.wikipedia.org/wiki/General_knowledge https://en.wikipedia.org/wiki/Zero-knowledge_proof From Wikipedia, the free encyclopedia "ZKP" redirects here. For the airport in Russia, see Zyryanka Airport. For other uses, see Zero knowledge. In cryptography, a zero-knowledge proof or zero-knowledge protocol is a method by which one party (the prover) can prove to another party (the verifier) that a given statement is true while the prover avoids conveying any additional information apart from the fact that the statement is indeed true. The essence of zero-knowledge proofs is that it is trivial to prove that one possesses knowledge of certain information by simply revealing it; the challenge is to prove such possession without revealing the information itself or any additional information.[1] If proving a statement requires that the prover possess some secret information, then the verifier will not be able to prove the statement to anyone else without possessing the secret information. The statement being proved must include the assertion that the prover has such knowledge, but without including or transmitting the knowledge itself in the assertion. Otherwise, the statement would not be proved in zero-knowledge because it provides the verifier with additional information about the statement by the end of the protocol. A zero-knowledge proof of knowledge is a special case when the statement consists only of the fact that the prover possesses the secret information. Interactive zero-knowledge proofs require interaction between the individual (or computer system) proving their knowledge and the individual validating the proof.[1] This section needs to be updated. The reason given is: There are also Non-interactive zero-knowledge proofs. Please help update this article to reflect recent events or newly available information. (December 2022) A protocol implementing zero-knowledge proofs of knowledge must necessarily require interactive input from the verifier. This interactive input is usually in the form of one or more challenges such that the responses from the prover will convince the verifier if and only if the statement is true, i.e., if the prover does possess the claimed knowledge. If this were not the case, the verifier could record the execution of the protocol and replay it to convince someone else that they possess the secret information. The new party's acceptance is either justified since the replayer does possess the information (which implies that the protocol leaked information, and thus, is not proved in zero-knowledge), or the acceptance is spurious, i.e., was accepted from someone who does not actually possess the information. Some forms of non-interactive zero-knowledge proofs exist,[2][3] but the validity of the proof relies on computational assumptions (typically the assumptions of an ideal cryptographic hash function). Abstract examples The Ali Baba cave Peggy randomly takes either path A or B, while Victor waits outside Victor chooses an exit path Peggy reliably appears at the exit Victor names There is a well-known story presenting the fundamental ideas of zero-knowledge proofs, first published in 1990 by Jean-Jacques Quisquater and others in their paper "How to Explain Zero-Knowledge Protocols to Your Children".[4] Using the common Alice and Bob anthropomorphic thought experiment placeholders, the two parties in a zero-knowledge proof are Peggy as the prover of the statement, and Victor, the verifier of the statement. In this story, Peggy has uncovered the secret word used to open a magic door in a cave. The cave is shaped like a ring, with the entrance on one side and the magic door blocking the opposite side. Victor wants to know whether Peggy knows the secret word; but Peggy, being a very private person, does not want to reveal her knowledge (the secret word) to Victor or to reveal the fact of her knowledge to the world in general. They label the left and right paths from the entrance A and B. First, Victor waits outside the cave as Peggy goes in. Peggy takes either path A or B; Victor is not allowed to see which path she takes. Then, Victor enters the cave and shouts the name of the path he wants her to use to return, either A or B, chosen at random. Providing she really does know the magic word, this is easy: she opens the door, if necessary, and returns along the desired path. However, suppose she did not know the word. Then, she would only be able to return by the named path if Victor were to give the name of the same path by which she had entered. Since Victor would choose A or B at random, she would have a 50% chance of guessing correctly. If they were to repeat this trick many times, say 20 times in a row, her chance of successfully anticipating all of Victor's requests would become very small (1 in 220, or very roughly 1 in a million). Thus, if Peggy repeatedly appears at the exit Victor names, he can conclude that it is extremely probable that Peggy does, in fact, know the secret word. One side note with respect to third-party observers: even if Victor is wearing a hidden camera that records the whole transaction, the only thing the camera will record is in one case Victor shouting "A!" and Peggy appearing at A or in the other case Victor shouting "B!" and Peggy appearing at B. A recording of this type would be trivial for any two people to fake (requiring only that Peggy and Victor agree beforehand on the sequence of A's and B's that Victor will shout). Such a recording will certainly never be convincing to anyone but the original participants. In fact, even a person who was present as an observer at the original experiment would be unconvinced, since Victor and Peggy might have orchestrated the whole "experiment" from start to finish. Further notice that if Victor chooses his A's and B's by flipping a coin on-camera, this protocol loses its zero-knowledge property; the on-camera coin flip would probably be convincing to any person watching the recording later. Thus, although this does not reveal the secret word to Victor, it does make it possible for Victor to convince the world in general that Peggy has that knowledge—counter to Peggy's stated wishes. However, digital cryptography generally "flips coins" by relying on a pseudo-random number generator, which is akin to a coin with a fixed pattern of heads and tails known only to the coin's owner. If Victor's coin behaved this way, then again it would be possible for Victor and Peggy to have faked the "experiment", so using a pseudo-random number generator would not reveal Peggy's knowledge to the world in the same way that using a flipped coin would. Notice that Peggy could prove to Victor that she knows the magic word, without revealing it to him, in a single trial. If both Victor and Peggy go together to the mouth of the cave, Victor can watch Peggy go in through A and come out through B. This would prove with certainty that Peggy knows the magic word, without revealing the magic word to Victor. However, such a proof could be observed by a third party, or recorded by Victor and such a proof would be convincing to anybody. In other words, Peggy could not refute such proof by claiming she colluded with Victor, and she is therefore no longer in control of who is aware of her knowledge. Two balls and the colour-blind friend Imagine your friend "Victor" is red-green colour-blind (while you are not) and you have two balls: one red and one green, but otherwise identical. To Victor, the balls seem completely identical. Victor is skeptical that the balls are actually distinguishable. You want to prove to Victor that the balls are in fact differently-coloured, but nothing else. In particular, you do not want to reveal which ball is the red one and which is the green. Here is the proof system. You give the two balls to Victor and he puts them behind his back. Next, he takes one of the balls and brings it out from behind his back and displays it. He then places it behind his back again and then chooses to reveal just one of the two balls, picking one of the two at random with equal probability. He will ask you, "Did I switch the ball?" This whole procedure is then repeated as often as necessary. By looking at the balls' colours, you can, of course, say with certainty whether or not he switched them. On the other hand, if the balls were the same colour and hence indistinguishable, there is no way you could guess correctly with probability higher than 50%. Since the probability that you would have randomly succeeded at identifying each switch/non-switch is 50%, the probability of having randomly succeeded at all switch/non-switches approaches zero ("soundness"). If you and your friend repeat this "proof" multiple times (e.g. 20 times), your friend should become convinced ("completeness") that the balls are indeed differently coloured. The above proof is zero-knowledge because your friend never learns which ball is green and which is red; indeed, he gains no knowledge about how to distinguish the balls.[5] Definition This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources in this section. Unsourced material may be challenged and removed. Find sources: "Zero-knowledge proof" – news · newspapers · books · scholar · JSTOR (July 2022) (Learn how and when to remove this template message) A zero-knowledge proof of some statement must satisfy three properties: Completeness: if the statement is true, an honest verifier (that is, one following the protocol properly) will be convinced of this fact by an honest prover. Soundness: if the statement is false, no cheating prover can convince an honest verifier that it is true, except with some small probability. Zero-knowledge: if the statement is true, no verifier learns anything other than the fact that the statement is true. In other words, just knowing the statement (not the secret) is sufficient to imagine a scenario showing that the prover knows the secret. This is formalized by showing that every verifier has some simulator that, given only the statement to be proved (and no access to the prover), can produce a transcript that "looks like" an interaction between an honest prover and the verifier in question. The first two of these are properties of more general interactive proof systems. The third is what makes the proof zero-knowledge.[6] Zero-knowledge proofs are not proofs in the mathematical sense of the term because there is some small probability, the soundness error, that a cheating prover will be able to convince the verifier of a false statement. In other words, zero-knowledge proofs are probabilistic "proofs" rather than deterministic proofs. However, there are techniques to decrease the soundness error to negligibly small values (e.g. guessing correctly on a hundred or thousand binary decisions has a 1 / 2^100 or 1/ 2^1000 soundness error, respectively. As the number of bits increases, soundness error decreases toward zero). A formal definition of zero-knowledge has to use some computational model, the most common one being that of a Turing machine. Let P P, V V, and S S be Turing machines. An interactive proof system with ( P , V ) {\displaystyle (P,V)} for a language L L is zero-knowledge if for any probabilistic polynomial time (PPT) verifier V ^ {\hat {V}} there exists a PPT simulator S S such that ∀ x ∈ L , z ∈ { 0 , 1 } ∗ , View V ^ ⁡ [ P ( x ) ↔ V ^ ( x , z ) ] = S ( x , z ) {\displaystyle \forall x\in L,z\in \{0,1\}^{*},\operatorname {View} _{\hat {V}}\left[P(x)\leftrightarrow {\hat {V}}(x,z)\right]=S(x,z)} where View V ^ ⁡ [ P ( x ) ↔ V ^ ( x , z ) ] {\displaystyle \operatorname {View} _{\hat {V}}\left[P(x)\leftrightarrow {\hat {V}}(x,z)\right]} is a record of the interactions between P ( x ) P(x) and V ^ ( x , z ) {\displaystyle {\hat {V}}(x,z)}. The prover P P is modeled as having unlimited computation power (in practice, P P usually is a probabilistic Turing machine). Intuitively, the definition states that an interactive proof system ( P , V ) {\displaystyle (P,V)} is zero-knowledge if for any verifier V ^ {\hat {V}} there exists an efficient simulator S S (depending on V ^ {\hat {V}}) that can reproduce the conversation between P P and V ^ {\hat {V}} on any given input. The auxiliary string z z in the definition plays the role of "prior knowledge" (including the random coins of V ^ {\hat {V}}). The definition implies that V ^ {\hat {V}} cannot use any prior knowledge string z z to mine information out of its conversation with P P, because if S S is also given this prior knowledge then it can reproduce the conversation between V ^ {\hat {V}} and P P just as before.[citation needed] The definition given is that of perfect zero-knowledge. Computational zero-knowledge is obtained by requiring that the views of the verifier V ^ {\hat {V}} and the simulator are only computationally indistinguishable, given the auxiliary string.[citation needed] Practical examples Discrete log of a given value We can apply these ideas to a more realistic cryptography application. Peggy wants to prove to Victor that she knows the discrete log of a given value in a given group.[7] For example, given a value y y, a large prime p p and a generator g g, she wants to prove that she knows a value x x such that g x mod p = y {\displaystyle g^{x}{\bmod {p}}=y}, without revealing x x. Indeed, knowledge of x x could be used as a proof of identity, in that Peggy could have such knowledge because she chose a random value x x that she didn't reveal to anyone, computed y = g x mod p {\displaystyle y=g^{x}{\bmod {p}}} and distributed the value of y y to all potential verifiers, such that at a later time, proving knowledge of x x is equivalent to proving identity as Peggy. The protocol proceeds as follows: in each round, Peggy generates a random number r r, computes C = g r mod p {\displaystyle C=g^{r}{\bmod {p}}} and discloses this to Victor. After receiving C C, Victor randomly issues one of the following two requests: he either requests that Peggy discloses the value of r r, or the value of ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}}. With either answer, Peggy is only disclosing a random value, so no information is disclosed by a correct execution of one round of the protocol. Victor can verify either answer; if he requested r r, he can then compute g r mod p {\displaystyle g^{r}{\bmod {p}}} and verify that it matches C C. If he requested ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}}, he can verify that C C is consistent with this, by computing g ( x + r ) mod ( p − 1 ) mod p {\displaystyle g^{(x+r){\bmod {(p-1)}}}{\bmod {p}}} and verifying that it matches ( C ⋅ y ) mod p {\displaystyle (C\cdot y){\bmod {p}}}. If Peggy indeed knows the value of x x, she can respond to either one of Victor's possible challenges. If Peggy knew or could guess which challenge Victor is going to issue, then she could easily cheat and convince Victor that she knows x x when she does not: if she knows that Victor is going to request r r, then she proceeds normally: she picks r r, computes C = g r mod p {\displaystyle C=g^{r}{\bmod {p}}} and discloses C C to Victor; she will be able to respond to Victor's challenge. On the other hand, if she knows that Victor will request ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}}, then she picks a random value r ′ r', computes C ′ = g r ′ ⋅ ( g x ) − 1 mod p {\displaystyle C'=g^{r'}\cdot \left(g^{x}\right)^{-1}{\bmod {p}}}, and discloses C ′ C' to Victor as the value of C C that he is expecting. When Victor challenges her to reveal ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}}, she reveals r ′ r', for which Victor will verify consistency, since he will in turn compute g r ′ mod p {\displaystyle g^{r'}{\bmod {p}}}, which matches C ′ ⋅ y C'\cdot y, since Peggy multiplied by the modular multiplicative inverse of y y. However, if in either one of the above scenarios Victor issues a challenge other than the one she was expecting and for which she manufactured the result, then she will be unable to respond to the challenge under the assumption of infeasibility of solving the discrete log for this group. If she picked r r and disclosed C = g r mod p {\displaystyle C=g^{r}{\bmod {p}}}, then she will be unable to produce a valid ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}} that would pass Victor's verification, given that she does not know x x. And if she picked a value r ′ r' that poses as ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}}, then she would have to respond with the discrete log of the value that she disclosed – but Peggy does not know this discrete log, since the value C she disclosed was obtained through arithmetic with known values, and not by computing a power with a known exponent. Thus, a cheating prover has a 0.5 probability of successfully cheating in one round. By executing a large enough number of rounds, the probability of a cheating prover succeeding can be made arbitrarily low. Short summary Peggy proves to know the value of x (for example her password). Peggy and Victor agree on a prime p p and a generator g g of the multiplicative group of the field Z p {\displaystyle \mathbb {Z} _{p}}. Peggy calculates the value y = g x mod p {\displaystyle y=g^{x}{\bmod {p}}} and transfers the value to Victor. The following two steps are repeated a (large) number of times. Peggy repeatedly picks a random value r ∈ U [ 0 , p − 2 ] {\displaystyle r\in U[0,p-2]} and calculates C = g r mod p {\displaystyle C=g^{r}{\bmod {p}}}. She transfers the value C C to Victor. Victor asks Peggy to calculate and transfer either the value ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}} or the value r r. In the first case Victor verifies ( C ⋅ y ) mod p ≡ g ( x + r ) mod ( p − 1 ) mod p {\displaystyle (C\cdot y){\bmod {p}}\equiv g^{(x+r){\bmod {(p-1)}}}{\bmod {p}}}. In the second case he verifies C ≡ g r mod p {\displaystyle C\equiv g^{r}{\bmod {p}}}. The value ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(}}p-1)} can be seen as the encrypted value of x mod ( p − 1 ) {\displaystyle x{\bmod {(}}p-1)}. If r r is truly random, equally distributed between zero and ( p − 2 ) {\displaystyle (p-2)}, this does not leak any information about x x (see one-time pad). Hamiltonian cycle for a large graph The following scheme is due to Manuel Blum.[8] In this scenario, Peggy knows a Hamiltonian cycle for a large graph G. Victor knows G but not the cycle (e.g., Peggy has generated G and revealed it to him.) Finding a Hamiltonian cycle given a large graph is believed to be computationally infeasible, since its corresponding decision version is known to be NP-complete. Peggy will prove that she knows the cycle without simply revealing it (perhaps Victor is interested in buying it but wants verification first, or maybe Peggy is the only one who knows this information and is proving her identity to Victor). To show that Peggy knows this Hamiltonian cycle, she and Victor play several rounds of a game. At the beginning of each round, Peggy creates H, a graph which is isomorphic to G (i.e. H is just like G except that all the vertices have different names). Since it is trivial to translate a Hamiltonian cycle between isomorphic graphs with known isomorphism, if Peggy knows a Hamiltonian cycle for G she also must know one for H. Peggy commits to H. She could do so by using a cryptographic commitment scheme. Alternatively, she could number the vertices of H. Next, for each edge of H, on a small piece of paper, she writes down the two vertices that the edge joins. Then she puts all these pieces of paper face down on a table. The purpose of this commitment is that Peggy is not able to change H while, at the same time, Victor has no information about H. Victor then randomly chooses one of two questions to ask Peggy. He can either ask her to show the isomorphism between H and G (see graph isomorphism problem), or he can ask her to show a Hamiltonian cycle in H. If Peggy is asked to show that the two graphs are isomorphic, she first uncovers all of H (e.g. by turning over all pieces of papers that she put on the table) and then provides the vertex translations that map G to H. Victor can verify that they are indeed isomorphic. If Peggy is asked to prove that she knows a Hamiltonian cycle in H, she translates her Hamiltonian cycle in G onto H and only uncovers the edges on the Hamiltonian cycle. This is enough for Victor to check that H does indeed contain a Hamiltonian cycle. It is important that the commitment to the graph be such that Victor can verify, in the second case, that the cycle is really made of edges from H. This can be done by, for example, committing to every edge (or lack thereof) separately. Completeness If Peggy does know a Hamiltonian cycle in G, she can easily satisfy Victor's demand for either the graph isomorphism producing H from G (which she had committed to in the first step) or a Hamiltonian cycle in H (which she can construct by applying the isomorphism to the cycle in G). Zero-knowledge Peggy's answers do not reveal the original Hamiltonian cycle in G. Each round, Victor will learn only H's isomorphism to G or a Hamiltonian cycle in H. He would need both answers for a single H to discover the cycle in G, so the information remains unknown as long as Peggy can generate a distinct H every round. If Peggy does not know of a Hamiltonian cycle in G, but somehow knew in advance what Victor would ask to see each round then she could cheat. For example, if Peggy knew ahead of time that Victor would ask to see the Hamiltonian cycle in H then she could generate a Hamiltonian cycle for an unrelated graph. Similarly, if Peggy knew in advance that Victor would ask to see the isomorphism then she could simply generate an isomorphic graph H (in which she also does not know a Hamiltonian cycle). Victor could simulate the protocol by himself (without Peggy) because he knows what he will ask to see. Therefore, Victor gains no information about the Hamiltonian cycle in G from the information revealed in each round. Soundness If Peggy does not know the information, she can guess which question Victor will ask and generate either a graph isomorphic to G or a Hamiltonian cycle for an unrelated graph, but since she does not know a Hamiltonian cycle for G she cannot do both. With this guesswork, her chance of fooling Victor is 2−n, where n is the number of rounds. For all realistic purposes, it is infeasibly difficult to defeat a zero-knowledge proof with a reasonable number of rounds in this way. Variants of zero-knowledge Different variants of zero-knowledge can be defined by formalizing the intuitive concept of what is meant by the output of the simulator "looking like" the execution of the real proof protocol in the following ways: We speak of perfect zero-knowledge if the distributions produced by the simulator and the proof protocol are distributed exactly the same. This is for instance the case in the first example above. Statistical zero-knowledge[9] means that the distributions are not necessarily exactly the same, but they are statistically close, meaning that their statistical difference is a negligible function. We speak of computational zero-knowledge if no efficient algorithm can distinguish the two distributions. Zero knowledge types Proof of knowledge: the knowledge is hidden in the exponent like in the example shown above. Pairing based cryptography: given f(x) and f(y), without knowing x and y, it is possible to compute f(x×y). Witness indistinguishable proof: verifiers cannot know which witness is used for producing the proof. Multi-party computation: while each party can keep their respective secret, they together produce a result. Ring signature: outsiders have no idea which key is used for signing. Applications Authentication systems Research in zero-knowledge proofs has been motivated by authentication systems where one party wants to prove its identity to a second party via some secret information (such as a password) but doesn't want the second party to learn anything about this secret. This is called a "zero-knowledge proof of knowledge". However, a password is typically too small or insufficiently random to be used in many schemes for zero-knowledge proofs of knowledge. A zero-knowledge password proof is a special kind of zero-knowledge proof of knowledge that addresses the limited size of passwords.[citation needed] In April 2015, the Sigma protocol (one-out-of-many proofs) was introduced.[10] In August 2021, Cloudflare, an American web infrastructure and security company decided to use the one-out-of-many proofs mechanism for private web verification using vendor hardware.[11] Ethical behavior One of the uses of zero-knowledge proofs within cryptographic protocols is to enforce honest behavior while maintaining privacy. Roughly, the idea is to force a user to prove, using a zero-knowledge proof, that its behavior is correct according to the protocol.[12][13] Because of soundness, we know that the user must really act honestly in order to be able to provide a valid proof. Because of zero knowledge, we know that the user does not compromise the privacy of its secrets in the process of providing the proof.[citation needed] Nuclear disarmament In 2016, the Princeton Plasma Physics Laboratory and Princeton University demonstrated a technique that may have applicability to future nuclear disarmament talks. It would allow inspectors to confirm whether or not an object is indeed a nuclear weapon without recording, sharing or revealing the internal workings which might be secret.[14] Blockchains Zero-knowledge proofs were applied in the Zerocoin and Zerocash protocols, which culminated in the birth of Zcoin[15] (later rebranded as Firo in 2020)[16] and Zcash cryptocurrencies in 2016. Zerocoin has a built-in mixing model that does not trust any peers or centralised mixing providers to ensure anonymity.[15] Users can transact in a base currency and can cycle the currency into and out of Zerocoins.[17] The Zerocash protocol uses a similar model (a variant known as a non-interactive zero-knowledge proof)[18] except that it can obscure the transaction amount, while Zerocoin cannot. Given significant restrictions of transaction data on the Zerocash network, Zerocash is less prone to privacy timing attacks when compared to Zerocoin. However, this additional layer of privacy can cause potentially undetected hyperinflation of Zerocash supply because fraudulent coins cannot be tracked.[15][19] In 2018, Bulletproofs were introduced. Bulletproofs are an improvement from non-interactive zero-knowledge proof where trusted setup is not needed.[20] It was later implemented into the Mimblewimble protocol (which the Grin and Beam cryptocurrencies are based upon) and Monero cryptocurrency.[21] In 2019, Firo implemented the Sigma protocol, which is an improvement on the Zerocoin protocol without trusted setup.[22][10] In the same year, Firo introduced the Lelantus protocol, an improvement on the Sigma protocol, where the former hides the origin and amount of a transaction.[23] History Zero-knowledge proofs were first conceived in 1985 by Shafi Goldwasser, Silvio Micali, and Charles Rackoff in their paper "The Knowledge Complexity of Interactive Proof-Systems".[12] This paper introduced the IP hierarchy of interactive proof systems (see interactive proof system) and conceived the concept of knowledge complexity, a measurement of the amount of knowledge about the proof transferred from the prover to the verifier. They also gave the first zero-knowledge proof for a concrete problem, that of deciding quadratic nonresidues mod m. Together with a paper by László Babai and Shlomo Moran, this landmark paper invented interactive proof systems, for which all five authors won the first Gödel Prize in 1993. In their own words, Goldwasser, Micali, and Rackoff say: Of particular interest is the case where this additional knowledge is essentially 0 and we show that [it] is possible to interactively prove that a number is quadratic non residue mod m releasing 0 additional knowledge. This is surprising as no efficient algorithm for deciding quadratic residuosity mod m is known when m’s factorization is not given. Moreover, all known NP proofs for this problem exhibit the prime factorization of m. This indicates that adding interaction to the proving process, may decrease the amount of knowledge that must be communicated in order to prove a theorem. The quadratic nonresidue problem has both an NP and a co-NP algorithm, and so lies in the intersection of NP and co-NP. This was also true of several other problems for which zero-knowledge proofs were subsequently discovered, such as an unpublished proof system by Oded Goldreich verifying that a two-prime modulus is not a Blum integer.[24] Oded Goldreich, Silvio Micali, and Avi Wigderson took this one step further, showing that, assuming the existence of unbreakable encryption, one can create a zero-knowledge proof system for the NP-complete graph coloring problem with three colors. Since every problem in NP can be efficiently reduced to this problem, this means that, under this assumption, all problems in NP have zero-knowledge proofs.[25] The reason for the assumption is that, as in the above example, their protocols require encryption. A commonly cited sufficient condition for the existence of unbreakable encryption is the existence of one-way functions, but it is conceivable that some physical means might also achieve it. On top of this, they also showed that the graph nonisomorphism problem, the complement of the graph isomorphism problem, has a zero-knowledge proof. This problem is in co-NP, but is not currently known to be in either NP or any practical class. More generally, Russell Impagliazzo and Moti Yung as well as Ben-Or et al. would go on to show that, also assuming one-way functions or unbreakable encryption, that there are zero-knowledge proofs for all problems in IP = PSPACE, or in other words, anything that can be proved by an interactive proof system can be proved with zero knowledge.[26][27] Not liking to make unnecessary assumptions, many theorists sought a way to eliminate the necessity of one way functions. One way this was done was with multi-prover interactive proof systems (see interactive proof system), which have multiple independent provers instead of only one, allowing the verifier to "cross-examine" the provers in isolation to avoid being misled. It can be shown that, without any intractability assumptions, all languages in NP have zero-knowledge proofs in such a system.[28] It turns out that in an Internet-like setting, where multiple protocols may be executed concurrently, building zero-knowledge proofs is more challenging. The line of research investigating concurrent zero-knowledge proofs was initiated by the work of Dwork, Naor, and Sahai.[29] One particular development along these lines has been the development of witness-indistinguishable proof protocols. The property of witness-indistinguishability is related to that of zero-knowledge, yet witness-indistinguishable protocols do not suffer from the same problems of concurrent execution.[30] Another variant of zero-knowledge proofs are non-interactive zero-knowledge proofs. Blum, Feldman, and Micali showed that a common random string shared between the prover and the verifier is enough to achieve computational zero-knowledge without requiring interaction.[2][3] Zero-Knowledge Proof protocols The most popular interactive or non-interactive zero-knowledge proof (e.g., zk-SNARK) protocols can be broadly categorized in the following four categories: Succinct Non-Interactive ARguments of Knowledge (SNARK), Scalable Transparent ARgument of Knowledge (STARK), Verifiable Polynomial Delegation (VPD), and Succinct Non-interactive ARGuments (SNARG). A list of zero-knowledge proof protocols and libraries is provided below along with comparisons based on transparency, universality, plausible post-quantum security, and programming paradigm.[31] A transparent protocol is one that does not require any trusted setup and uses public randomness. A universal protocol is one that does not require a separate trusted setup for each circuit. Finally, a plausibly post-quantum protocol is one that is not susceptible to known attacks involving quantum algorithms. Zero-knowledge proof (ZKP) systems ZKP System Publication year Protocol Transparent Universal Plausibly Post-Quantum Secure Programming Paradigm Pinocchio[32] 2013 zk-SNARK No No No Procedural Geppetto[33] 2015 zk-SNARK No No No Procedural TinyRAM[34] 2013 zk-SNARK No No No Procedural Buffet[35] 2015 zk-SNARK No No No Procedural ZoKrates[36] 2018 zk-SNARK No No No Procedural xJsnark[37] 2018 zk-SNARK No No No Procedural vRAM[38] 2018 zk-SNARG No Yes No Assembly vnTinyRAM[39] 2014 zk-SNARK No Yes No Procedural MIRAGE[40] 2020 zk-SNARK No Yes No Arithmetic Circuits Sonic[41] 2019 zk-SNARK No Yes No Arithmetic Circuits Marlin[42] 2020 zk-SNARK No Yes No Arithmetic Circuits PLONK[43] 2019 zk-SNARK No Yes No Arithmetic Circuits SuperSonic[44] 2020 zk-SNARK Yes Yes No Arithmetic Circuits Bulletproofs[20] 2018 Bulletproofs Yes Yes No Arithmetic Circuits Hyrax[45] 2018 zk-SNARK Yes Yes No Arithmetic Circuits Halo[46] 2019 zk-SNARK Yes Yes No Arithmetic Circuits Virgo[47] 2020 zk-SNARK Yes Yes Yes Arithmetic Circuits Ligero[48] 2017 zk-SNARK Yes Yes Yes Arithmetic Circuits Aurora[49] 2019 zk-SNARK Yes Yes Yes Arithmetic Circuits zk-STARK[50] 2019 zk-STARK Yes Yes Yes Assembly Zilch[31] 2021 zk-STARK Yes Yes Yes Object-Oriented See also Arrow information paradox Cryptographic protocol Feige–Fiat–Shamir identification scheme Proof of knowledge Topics in cryptography Witness-indistinguishable proof Zero-knowledge password proof Non-interactive zero-knowledge proof References "What is a zero-knowledge proof and why is it useful?". 16 November 2017. 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Cryptology ePrint Archive. Maller, Mary; Bowe, Sean; Kohlweiss, Markulf; Meiklejohn, Sarah (6 November 2019). "Sonic: Zero-Knowledge SNARKs from Linear-Size Universal and Updatable Structured Reference Strings". Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security. Association for Computing Machinery: 2111–2128. doi:10.1145/3319535.3339817. hdl:20.500.11820/739b94f1-54f0-4ec3-9644-3c95eea1e8f5. S2CID 242772913. Chiesa, Alessandro; Hu, Yuncong; Maller, Mary; Mishra, Pratyush; Vesely, Noah; Ward, Nicholas (2020). "Marlin: Preprocessing zkSNARKs with Universal and Updatable SRS". Advances in Cryptology – EUROCRYPT 2020. Lecture Notes in Computer Science. Springer International Publishing. 12105: 738–768. doi:10.1007/978-3-030-45721-1_26. ISBN 978-3-030-45720-4. S2CID 204772154. Gabizon, Ariel; Williamson, Zachary J.; Ciobotaru, Oana (2019). "PLONK: Permutations over Lagrange-bases for Oecumenical Noninteractive arguments of Knowledge". Cryptology ePrint Archive. Bünz, Benedikt; Fisch, Ben; Szepieniec, Alan (2020). "Transparent SNARKs from DARK Compilers". Advances in Cryptology – EUROCRYPT 2020. Lecture Notes in Computer Science. Springer International Publishing. 12105: 677–706. doi:10.1007/978-3-030-45721-1_24. ISBN 978-3-030-45720-4. S2CID 204892714. Wahby, Riad S.; Tzialla, Ioanna; Shelat, Abhi; Thaler, Justin; Walfish, Michael (May 2018). "Doubly-Efficient zkSNARKs Without Trusted Setup". 2018 IEEE Symposium on Security and Privacy (SP): 926–943. doi:10.1109/SP.2018.00060. ISBN 978-1-5386-4353-2. Bowe, Sean; Grigg, Jack; Hopwood, Daira (2019). "Recursive Proof Composition without a Trusted Setup". Cryptology ePrint Archive. Zhang, Jiaheng; Xie, Tiancheng; Zhang, Yupeng; Song, Dawn (May 2020). "Transparent Polynomial Delegation and Its Applications to Zero Knowledge Proof". 2020 IEEE Symposium on Security and Privacy (SP): 859–876. doi:10.1109/SP40000.2020.00052. ISBN 978-1-7281-3497-0. Ames, Scott; Hazay, Carmit; Ishai, Yuval; Venkitasubramaniam, Muthuramakrishnan (30 October 2017). "Ligero: Lightweight Sublinear Arguments Without a Trusted Setup". Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security. Association for Computing Machinery: 2087–2104. doi:10.1145/3133956.3134104. ISBN 9781450349468. S2CID 5348527. Ben-Sasson, Eli; Chiesa, Alessandro; Riabzev, Michael; Spooner, Nicholas; Virza, Madars; Ward, Nicholas P. (2019). "Aurora: Transparent Succinct Arguments for R1CS". Advances in Cryptology – EUROCRYPT 2019. Lecture Notes in Computer Science. Springer International Publishing. 11476: 103–128. doi:10.1007/978-3-030-17653-2_4. ISBN 978-3-030-17652-5. S2CID 52832327. Ben-Sasson, Eli; Bentov, Iddo; Horesh, Yinon; Riabzev, Michael (2019). "Scalable Zero Knowledge with No Trusted Setup". Advances in Cryptology – CRYPTO 2019. Lecture Notes in Computer Science. Springer International Publishing. 11694: 701–732. doi:10.1007/978-3-030-26954-8_23. ISBN 978-3-030-26953-1. S2CID 199501907. Categories: Theory of cryptographyZero-knowledge protocols https://en.wikipedia.org/wiki/Zero-knowledge_proof https://en.wikipedia.org/wiki/List_of_knowledge_deities Category:Zero-knowledge protocols Category Talk Read Edit View history Tools Help From Wikipedia, the free encyclopedia The main article for this category is Zero-knowledge protocol. Pages in category "Zero-knowledge protocols" The following 6 pages are in this category, out of 6 total. This list may not reflect recent changes. A Anonymous veto network C Commitment scheme D Dining cryptographers problem F Feige–Fiat–Shamir identification scheme O Open vote network Z Zero-knowledge proof Categories: Asymmetric-key algorithmsCryptographic protocols https://en.wikipedia.org/wiki/Category:Zero-knowledge_protocols https://en.wikipedia.org/wiki/Law_of_Demeter https://en.wikipedia.org/wiki/Slack_(software) https://en.wikipedia.org/wiki/Uncommon_Knowledge https://en.wikipedia.org/wiki/Threshold_knowledge https://en.wikipedia.org/wiki/Timeline_of_knowledge_about_galaxies,_clusters_of_galaxies,_and_large-scale_structure https://en.wikipedia.org/wiki/Innatism https://en.wikipedia.org/wiki/Rationalism#The_innate_knowledge_thesis https://en.wikipedia.org/wiki/House_of_Knowledge https://en.wikipedia.org/wiki/Knowledge_Quarter https://en.wikipedia.org/wiki/Consilience_(book) https://en.wikipedia.org/wiki/Socrates#Virtue_and_knowledge https://en.wikipedia.org/wiki/Relativism https://en.wikipedia.org/wiki/Vidya_(philosophy) https://en.wikipedia.org/wiki/Knowledge_production_modes https://en.wikipedia.org/wiki/Local_knowledge_problem https://en.wikipedia.org/wiki/The_Postmodern_Condition https://en.wikipedia.org/wiki/Knowledge_translation https://en.wikipedia.org/wiki/Braiding_Sweetgrass https://en.wikipedia.org/wiki/Democratization_of_knowledge https://en.wikipedia.org/wiki/Knowledge_gap_hypothesis https://en.wikipedia.org/wiki/Certainty https://en.wikipedia.org/wiki/STOCK_Act https://en.wikipedia.org/wiki/Knowledge_Is_King https://en.wikipedia.org/wiki/Semantic_Scholar https://en.wikipedia.org/wiki/Knowledge_broker https://en.wikipedia.org/wiki/Route_knowledge https://en.wikipedia.org/wiki/Knowledge-based_processor https://en.wikipedia.org/wiki/Forbidden_knowledge https://en.wikipedia.org/wiki/Wikidata https://en.wikipedia.org/wiki/Encyclopedic_knowledge https://en.wikipedia.org/wiki/Knowledge_space https://en.wikipedia.org/wiki/Knowledge_level https://en.wikipedia.org/wiki/The_Sword_of_Knowledge https://en.wikipedia.org/wiki/Schema_(psychology) https://en.wikipedia.org/wiki/Pedagogy https://en.wikipedia.org/wiki/Experiential_knowledge https://en.wikipedia.org/wiki/Postmodernism https://en.wikipedia.org/wiki/Core_Knowledge https://en.wikipedia.org/wiki/Prop%C3%A6dia#Outline_of_Knowledge https://en.wikipedia.org/wiki/Karl_Popper https://en.wikipedia.org/wiki/Michel_Foucault https://en.wikipedia.org/wiki/Access_to_Knowledge_movement https://en.wikipedia.org/wiki/Hutter_Prize https://en.wikipedia.org/wiki/SECI_model_of_knowledge_dimensions https://en.wikipedia.org/wiki/Consilience_(book) https://en.wikipedia.org/wiki/Everyman_(15th-century_play) https://en.wikipedia.org/wiki/Abhij%C3%B1%C4%81 https://en.wikipedia.org/wiki/Ismail_al-Jazari https://en.wikipedia.org/wiki/Traditional_ecological_knowledge https://en.wikipedia.org/wiki/Pseudoscience https://en.wikipedia.org/wiki/Empiricism https://en.wikipedia.org/wiki/Scientist https://en.wikipedia.org/wiki/An_Essay_on_Criticism https://en.wikipedia.org/wiki/Ornithology#Early_knowledge_and_study https://en.wikipedia.org/wiki/Technological_pedagogical_content_knowledge https://en.wikipedia.org/wiki/Knowledge_Generation_Bureau https://en.wikipedia.org/wiki/University https://en.wikipedia.org/wiki/Knowledge_compilation https://en.wikipedia.org/wiki/Sherlock_Holmes#Knowledge_and_skills https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction https://en.wikipedia.org/wiki/Tree_of_Knowledge_(Australia) https://en.wikipedia.org/wiki/Vocabulary#Productive_and_receptive_knowledge https://en.wikipedia.org/wiki/Appropriation_of_knowledge https://en.wikipedia.org/wiki/Skepticism https://en.wikipedia.org/wiki/Bioprospecting https://en.wikipedia.org/wiki/Frame_(artificial_intelligence)#Frame_language https://en.wikipedia.org/wiki/Mathematical_knowledge_management https://en.wikipedia.org/wiki/Texas_Assessment_of_Knowledge_and_Skills https://en.wikipedia.org/wiki/Augustine_of_Hippo#Natural_knowledge_and_biblical_interpretation https://en.wikipedia.org/wiki/W._Edwards_Deming#The_Deming_System_of_Profound_Knowledge https://en.wikipedia.org/wiki/Follow-the-sun https://en.wikipedia.org/wiki/Non-interactive_zero-knowledge_proof https://en.wikipedia.org/wiki/Terry_Scott_Taylor#Knowledge_&_Innocence https://en.wikipedia.org/wiki/Omniscience https://en.wikipedia.org/wiki/Invention_of_Knowledge https://en.wikipedia.org/wiki/Theaetetus_(dialogue)#Protagoras%27_theory_of_knowledge https://en.wikipedia.org/wiki/Knowledge_neglect https://en.wikipedia.org/wiki/Scientia_sacra https://en.wikipedia.org/wiki/Knowledge_and_Decisions https://en.wikipedia.org/wiki/Proof_of_knowledge https://en.wikipedia.org/wiki/Factual_relativism https://en.wikipedia.org/wiki/Knowledge_Query_and_Manipulation_Language https://en.wikipedia.org/wiki/Knowledge-based_engineering https://en.wikipedia.org/wiki/Multi-factor_authentication https://en.wikipedia.org/wiki/Knowledge_survey https://en.wikipedia.org/wiki/Intellectual_capital https://en.wikipedia.org/wiki/Transcendentalism#Transcendental_knowledge https://en.wikipedia.org/wiki/Theory_of_knowledge_(disambiguation) https://en.wikipedia.org/wiki/A_Culture_of_Conspiracy https://en.wikipedia.org/wiki/A_Treatise_Concerning_the_Principles_of_Human_Knowledge https://en.wikipedia.org/wiki/Objectivity_(philosophy) https://en.wikipedia.org/wiki/Knowledge_regime https://en.wikipedia.org/wiki/The_Social_Construction_of_Reality https://en.wikipedia.org/wiki/Francis_Bacon#Organization_of_knowledge https://en.wikipedia.org/wiki/Knowledge-based_recommender_system https://en.wikipedia.org/wiki/Traditional_medicine#Knowledge_transmission_and_creation https://en.wikipedia.org/wiki/Information_silo https://en.wikipedia.org/wiki/World_Bank#Global_Operations_Knowledge_Management_Unit https://en.wikipedia.org/wiki/Philosophical_skepticism https://en.wikipedia.org/wiki/The_Knowledge:_How_to_Rebuild_Our_World_from_Scratch https://en.wikipedia.org/wiki/Bayes%27_theorem?wprov=srpw1_412 https://en.wikipedia.org/wiki/Mathematician https://en.wikipedia.org/wiki/Zoology https://en.wikipedia.org/wiki/Adam_and_Eve https://en.wikipedia.org/wiki/Foundations_of_the_Science_of_Knowledge https://en.wikipedia.org/wiki/Unity_of_science https://en.wikipedia.org/wiki/Nihilism https://en.wikipedia.org/wiki/Tabula_rasa Meaning of knowledge Linguistic According to the Oxford English Dictionary, the word knowledge refers to "Facts, information, and skills acquired through experience or education; the theoretical or practical understanding of a subject." "In this work on the concept of knowledge, Franz Rosenthal collected a number of definitions of 'ilm, organizing them according to what he saw as their essential elements (admitting that the list was ahistorical and did not necessarily conform to categories the medieval Muslim scholars themselves would have used). Among these definitions, we find the following: Knowledge is the process of knowing, and identical with the knower and the known. Knowledge is that through which one knows. Knowledge is that through which the essence is knowing. Knowledge is that through which the knower is knowing. Knowledge is that which necessitates for him in whom it subsists the name of knower. Knowledge is that which necessitates that he in whom it subsists is knowing. Knowledge is that which necessitates that he in whom it resides (mahall) is knowing. Knowledge stands for ( 'ibarah 'an) the object known ( 'al-ma lum). Knowledge is but the concepts known ( 'al-ma ani al-ma luma). Knowledge is the mentally existing object."[1] Islamic meaning Knowledge in the Western world means information about something, divine or corporeal, while In Islamic point of view 'ilm is an all-embracing term covering theory, action and education, it is not confined to the acquisition of knowledge only, but also embraces socio-political and moral aspects.it requires insight, commitment to the goals of Islam and for the believers to act upon their belief.[2] Also it is reported in hadith that "Knowledge is not extensive learning. Rather, it is a light that God casts in the heart of whomever He wills." [3] https://en.wikipedia.org/wiki/Ilm_(Arabic)#Meaning_of_knowledge https://en.wikipedia.org/wiki/Scientific_Knowledge_and_Its_Social_Problems https://en.wikipedia.org/wiki/Citation https://en.wikipedia.org/wiki/Problem_solving https://en.wikipedia.org/wiki/Modern_flat_Earth_beliefs https://en.wikipedia.org/wiki/Generosity#In_knowledge https://en.wikipedia.org/wiki/Amnesia https://en.wikipedia.org/wiki/Spherical_Earth https://en.wikipedia.org/wiki/Library_Genesis https://en.wikipedia.org/wiki/Third_eye https://en.wikipedia.org/wiki/International_Service_for_the_Acquisition_of_Agri-biotech_Applications#Global_Knowledge_Center_on_Crop_Biotechnology https://en.wikipedia.org/wiki/WolframAlpha https://en.wikipedia.org/wiki/Knowledge-based_authentication https://en.wikipedia.org/wiki/Pre-Socratic_philosophy#Knowledge https://en.wikipedia.org/wiki/Reinforcement_learning https://en.wikipedia.org/wiki/Magician_(fantasy) https://en.wikipedia.org/wiki/Physicist https://en.wikipedia.org/wiki/Test_of_Economic_Knowledge https://en.wikipedia.org/wiki/Precognition https://en.wikipedia.org/wiki/Basic_research https://en.wikipedia.org/wiki/Methodology https://en.wikipedia.org/wiki/Experience https://en.wikipedia.org/wiki/Mens_rea https://en.wikipedia.org/wiki/Schaff%E2%80%93Herzog_Encyclopedia_of_Religious_Knowledge https://en.wikipedia.org/wiki/The_Secret_Knowledge https://en.wikipedia.org/wiki/Penny_Cyclopaedia#National_Cyclopedia_of_Useful_Knowledge https://en.wikipedia.org/wiki/Non-monotonic_logic https://en.wikipedia.org/wiki/Sustainable_Development_Goals https://en.wikipedia.org/wiki/Cognitive_psychology https://en.wikipedia.org/wiki/Human_behavior https://en.wikipedia.org/wiki/Coloniality_of_power#Systems_of_knowledge https://en.wikipedia.org/wiki/Printing https://en.wikipedia.org/wiki/The_Way_to_Divine_Knowledge https://en.wikipedia.org/wiki/Waldwissen https://en.wikipedia.org/wiki/Non-disclosure_agreement https://en.wikipedia.org/wiki/Lexicon https://en.wikipedia.org/wiki/Noble_Eightfold_Path https://en.wikipedia.org/wiki/If_a_tree_falls_in_a_forest#Knowledge_of_the_unobserved_world https://en.wikipedia.org/wiki/History_of_science https://en.wikipedia.org/wiki/Hematology https://en.wikipedia.org/wiki/Justification_(epistemology)#Justification_and_knowledge https://en.wikipedia.org/wiki/Discourse https://en.wikipedia.org/wiki/Unity_of_knowledge_and_action https://en.wikipedia.org/wiki/Tartary https://en.wikipedia.org/wiki/Philanthropedia https://en.wikipedia.org/wiki/Visualization_(graphics) https://en.wikipedia.org/wiki/Nightingale_Pledge https://en.wikipedia.org/wiki/Doctor_of_Science https://en.wikipedia.org/wiki/Expert_system https://en.wikipedia.org/wiki/Walker%27s_Hibernian_Magazine https://en.wikipedia.org/wiki/Critical_theory https://en.wikipedia.org/wiki/Scientific_management https://en.wikipedia.org/wiki/Autodidacticism https://en.wikipedia.org/wiki/Occult https://en.wikipedia.org/wiki/FlatWorld https://en.wikipedia.org/wiki/Paradigm_shift https://en.wikipedia.org/wiki/History_of_mathematics https://en.wikipedia.org/wiki/War_for_talent#Knowledge_work https://en.wikipedia.org/wiki/Technocracy https://en.wikipedia.org/wiki/Supernatural https://en.wikipedia.org/wiki/Fall_of_man https://en.wikipedia.org/wiki/Anthroposophy#Spiritual_knowledge_and_freedom https://en.wikipedia.org/wiki/Aladdin_Knowledge_Systems https://en.wikipedia.org/wiki/Streetwise https://en.wikipedia.org/wiki/List_of_musical_instruments https://en.wikipedia.org/wiki/Celestial_Emporium_of_Benevolent_Knowledge https://en.wikipedia.org/wiki/Analytic_philosophy https://en.wikipedia.org/wiki/Maxim_(philosophy)#Personal_knowledge https://en.wikipedia.org/wiki/Second_language#Depth_of_knowledge https://en.wikipedia.org/wiki/Moksha https://en.wikipedia.org/wiki/Mutual_knowledge https://en.wikipedia.org/wiki/Diffusion_of_innovations https://en.wikipedia.org/wiki/Hinterland#Breadth_of_knowledge https://en.wikipedia.org/wiki/Rhetoric#Knowledge https://en.wikipedia.org/wiki/Consistency_(knowledge_bases) https://en.wikipedia.org/wiki/Innocence#In_relation_to_knowledge https://en.wikipedia.org/wiki/World_of_Knowledge https://en.wikipedia.org/wiki/Intelligence_agency https://en.wikipedia.org/wiki/Contamination https://en.wikipedia.org/wiki/Positivism https://en.wikipedia.org/wiki/Hockney%E2%80%93Falco_thesis https://en.wikipedia.org/wiki/Paradise_Lost https://en.wikipedia.org/wiki/Ethics https://en.wikipedia.org/wiki/Engineering https://en.wikipedia.org/wiki/School https://en.wikipedia.org/wiki/Christian_mysticism#False_spiritual_knowledge https://en.wikipedia.org/wiki/Human%E2%80%93computer_interaction#Knowledge-driven_human%E2%80%93computer_interaction https://en.wikipedia.org/wiki/Notice#Notice_and_knowledge https://en.wikipedia.org/wiki/Falsifiability https://en.wikipedia.org/wiki/Fionn_mac_Cumhaill https://en.wikipedia.org/wiki/Outline_of_epistemology https://en.wikipedia.org/wiki/Cognitive_robotics#Knowledge_acquisition https://en.wikipedia.org/wiki/Writing#Scientific_and_scholarly_knowledge_production https://en.wikipedia.org/wiki/Is%E2%80%93ought_problem https://en.wikipedia.org/wiki/The_Degrees_of_Knowledge https://en.wikipedia.org/wiki/Genetic_epistemology#Types_of_knowledge https://en.wikipedia.org/wiki/The_Universal_Magazine_of_Knowledge_and_Pleasure https://en.wikipedia.org/wiki/Divergent_(novel)#Social_structure_and_knowledge https://en.wikipedia.org/wiki/Anti-pattern https://en.wikipedia.org/wiki/Compendium

Category:Phonetic transcription symbols

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Pages in category "Phonetic transcription symbols"

The following 109 pages are in this category, out of 109 total. This list may not reflect recent changes.

A

• Ȧ
• Ă
• Ā
• Ã
• Æ
• Latin alpha

B

• Ɓ
• Ƀ
• Small capital B
• Beta
• Bilabial click

C

• Ç
• Ć
• Ċ
• Č
• Ƈ
• Stretched C
• Ȼ
• C with bar
• Chi (letter)
• Click letter

D

• Ḍ
• African D
• Ɗ
• D with hook and tail
• D with stroke
• Eth
• Db ligature
• Double grave accent

E

• Ẽ
• Ə
• Eng (letter)
• Latin epsilon

G

• Ǧ
• Ġ
• Insular G
• Ɠ
• Glottal stop (letter)
• Gamma
• Latin gamma

ɡ

• ꬶ

H

• Ḫ
• Heng (letter)
• H with stroke
• Turned h with fishhook
• Ḥ

I

• Ɨ
• Ɪ
• Latin iota

J

• J̌

K

• K with diagonal stroke
• Ƙ
• K with stroke
• K with stroke and diagonal stroke

L

• Ł
• Barred lambda
• Latin beta
• Latin turned alpha

M

• Ɱ
• Modifier letter left half ring
• Modifier letter right half ring

N

• Ñ
• N with long right leg
• Ɲ

O

• Ɵ
• Ö
• Ǫ
• Ø
• Œ
• ⱺ
• Open O

P

• P with stroke
• Ƥ
• Palatal hook
• Phonetic Symbol Guide

Q

• Q with stroke
• Qp ligature

R

• Ȓ
• R with tail

S

• S͎
• S with swash tail
• Š
• Ṡ
• S̀
• Esh (letter)

T

• Ƭ
• Ʈ
• Theta
• Tie (typography)
• Turned A
• Turned h

U

• U bar
• Ŭ

V

• V with diagonal stroke
• Ʋ
• Turned v
• V with curl
• Voiced labiodental flap

W

• Ɯ

X

• X̣

Y

• Ý
• Ÿ (vowel)
• Yogh

Z

• Z with swash tail
• Ezh
• Ź
• Ž
• Z̀
• Ǯ

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• Phonetic alphabets

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https://en.wikipedia.org/wiki/Category:Phonetic_transcription_symbols

In linguistics, a count noun (also countable noun) is a noun that can be modified by a quantity and that occurs in both singular and plural forms, and that can co-occur with quantificational determiners like every, each, several, etc. A mass noun has none of these properties: It cannot be modified by a number, cannot occur in plural, and cannot co-occur with quantificational determiners. 

https://en.wikipedia.org/wiki/Count_noun

A determiner, also called determinative (abbreviated DET), is a word, phrase, or affix that occurs together with a noun or noun phrase and generally serves to express the reference of that noun or noun phrase in the context. That is, a determiner may indicate whether the noun is referring to a definite or indefinite element of a class, to a closer or more distant element, to an element belonging to a specified person or thing, to a particular number or quantity, etc. Common kinds of determiners include definite and indefinite articles (the, a), demonstratives (this, that), possessive determiners (my, their), cardinal numerals (one, two), quantifiers (many, both), distributive determiners (each, every), and interrogative determiners (which, what). 

For the written element in logographic scripts, see Determinative.

 

https://en.wikipedia.org/wiki/Determiner

 

 

In linguistics, definiteness is a semantic feature of noun phrases, distinguishing between referents or senses that are identifiable in a given context (definite noun phrases) and those which are not (indefinite noun phrases). The prototypical definite noun phrase picks out a unique, familiar, specific referent such as the sun or Australia, as opposed to indefinite examples like an idea or some fish.

There is considerable variation in the expression of definiteness across languages, and some languages such as Japanese do not generally mark it so that the same expression could be definite in some contexts and indefinite in others. In other languages, such as English, it is usually marked by the selection of determiner (e.g., the vs a). In still other languages, such as Danish, definiteness is marked morphologically. 

https://en.wikipedia.org/wiki/Definiteness

 

 

Iron meteorites, also called siderites or ferrous meteorites, are a type of meteorite that consist overwhelmingly of an iron–nickel alloy known as meteoric iron that usually consists of two mineral phases: kamacite and taenite. Most iron meteorites originate from cores of planetesimals,^[2] with the exception of the IIE iron meteorite group^[3]

The iron found in iron meteorites was one of the earliest sources of usable iron available to humans, due to the malleability and ductility of the meteoric iron,^[4] before the development of smelting that signaled the beginning of the Iron Age. 

Iron meteorite
— Type —
Tamentit Iron Meteorite, found in 1864 in the Sahara,[1] weighing about 500 kg (1,100 lb). On display at Vulcania park in France.

https://en.wikipedia.org/wiki/Iron_meteorite

Count-classifiers and mass-classifiers

A classifier categorizes a class of nouns by picking out some salient perceptual properties...which are permanently associated with entities named by the class of nouns; a measure word does not categorize but denotes the quantity of the entity named by a noun.

— Tai (1994, p. 2), emphasis added

Within the set of nominal classifiers, linguists generally draw a distinction between "count-classifiers" and "mass-classifiers". True count-classifiers^{[note 8]} are used for naming or counting a single count noun,^[15] and have no direct translation in English; for example, 一本书 (yì běn shū, one-CL book) can only be translated in English as "one book" or "a book".^[20] Furthermore, count-classifiers cannot be used with mass nouns: just as an English speaker cannot ordinarily say *"five muds", a Chinese speaker cannot say *五个泥 (wǔ ge nì, five-CL mud). For such mass nouns, one must use mass-classifiers.^{[15][note 9]}

Mass-classifiers (true measure words) do not pick out inherent properties of an individual noun like count-classifiers do; rather, they lump nouns into countable units. Thus, mass-classifiers can generally be used with multiple types of nouns; for example, while the mass-classifier 盒 (hé, box) can be used to count boxes of lightbulbs (一盒灯泡 yì hé dēngpào, "one box of lightbulbs") or of books (一盒教材 yì hé jiàocái, "one box of textbooks"), each of these nouns must use a different count-classifier when being counted by itself (一盏灯泡 yì zhǎn dēngpào "one lightbulb"; vs. 一本教材 yì běn jiàocái "one textbook"). While count-classifiers have no direct English translation, mass-classifiers often do: phrases with count-classifiers such as 一个人 (yí ge rén, one-CL person) can only be translated as "one person" or "a person", whereas those with mass-classifiers such as 一群人 (yì qún rén, one-crowd-person) can be translated as "a crowd of people". All languages, including English, have mass-classifiers, but count-classifiers are unique to certain "classifier languages", and are not a part of English grammar apart from a few exceptional cases such as head of livestock.^[21]

Within the range of mass-classifiers, authors have proposed subdivisions based on the manner in which a mass-classifier organizes the noun into countable units. One of these is measurement units (also called "standard measures"),^[22] which all languages must have in order to measure items; this category includes units such as kilometers, liters, or pounds^[23] (see list). Like other classifiers, these can also stand without a noun; thus, for example, 磅 (bàng, pound) may appear as both 三磅肉 (sān bàng ròu, "three pounds of meat") or just 三磅 (sān bàng, "three pounds", never *三个磅 sān ge bàng).^[24] Units of currency behave similarly: for example, 十元 (shí yuán, "ten yuan"), which is short for (for example) 十元人民币 (shí yuán rénmínbì, "ten units of renminbi"). Other proposed types of mass-classifiers include "collective"^{[25][note 10]} mass-classifiers, such as 一群人 (yì qún rén, "a crowd of people"), which group things less precisely; and "container"^[26] mass-classifiers which group things by containers they come in, as in 一碗粥 (yì wǎn zhōu, "a bowl of porridge") or 一包糖 (yì bāo táng, "a bag of sugar").

The difference between count-classifiers and mass-classifiers can be described as one of quantifying versus categorizing: in other words, mass-classifiers create a unit by which to measure something (i.e. boxes, groups, chunks, pieces, etc.), whereas count-classifiers simply name an existing item.^[27] Most words can appear with both count-classifiers and mass-classifiers; for example, pizza can be described as both 一张比萨 (yì zhāng bǐsà, "one pizza", literally "one pie of pizza"), using a count-classifier, and as 一块比萨 (yí kuài bǐsà, "one piece of pizza"), using a mass-classifier. In addition to these semantic differences, there are differences in the grammatical behaviors of count-classifiers and mass-classifiers;^[28] for example, mass-classifiers may be modified by a small set of adjectives (as in 一大群人 yí dà qún rén, "a big crowd of people"), whereas count-classifiers usually may not (for example, *一大个人 yí dà ge rén is never said for "a big person"; instead the adjective must modify the noun: 一个大人 yí ge dà rén).^[29] Another difference is that count-classifiers may often be replaced by a "general" classifier 个 (個), gè with no apparent change in meaning, whereas mass-classifiers may not.^[30] Syntacticians Lisa Cheng and Rint Sybesma propose that count-classifiers and mass-classifiers have different underlying syntactic structures, with count-classifiers forming "classifier phrases",^{[note 11]} and mass-classifiers being a sort of relative clause that only looks like a classifier phrase.^[31] The distinction between count-classifiers and mass-classifiers is often unclear, however, and other linguists have suggested that count-classifiers and mass-classifiers may not be fundamentally different. They posit that "count-classifier" and "mass-classifier" are the extremes of a continuum, with most classifiers falling somewhere in between.^[32]

Verbal classifiers

There is a set of "verbal classifiers" used specifically for counting the number of times an action occurs, rather than counting a number of items; this set includes 次 cì, 遍/徧 biàn, 回 huí, and 下 xià, which all roughly translate to "times".^[33] For example, 我去过三次北京 (wǒ qù-guo sān cì Běijīng, I go-PAST three-CL Beijing, "I have been to Beijing three times").^[34] These words can also form compound classifiers with certain nouns, as in 人次 rén cì "person-time", which can be used to count (for example) visitors to a museum in a year (where visits by the same person on different occasions are counted separately).

Another type of verbal classifier indicates the tool or implement used to perform the action. An example is found in the sentence 他踢了我一脚 tā tī le wǒ yī jiǎo "he kicked me", or more literally "he kicked me one foot". The word 脚 jiǎo, which usually serves as a simple noun meaning "foot", here functions as a verbal classifier reflecting the tool (namely the foot) used to perform the kicking action.

Relation to nouns

鱼 yú
"fish"

裤子 kùzi
"(pair of) pants"

河 hé
"river"

凳子 dèngzi
"long bench"

The above nouns denoting long or flexible objects may all appear with the classifier 条 (條) tiáo in certain dialects such as Mandarin.^[35] In Mandarin, 一条板凳 means "a CL bench", and if people want to say "a chair", 個/个 or 張/张 is used because 条 is only used for referring to relatively long things. In other dialects such as Cantonese, 條 cannot be used to refer to 櫈. Instead, 張 is used.

Different classifiers often correspond to different particular nouns. For example, books generally take the classifier 本 běn, flat objects take 张 (張) zhāng, animals take 只 (隻) zhī, machines take 台 tái, large buildings and mountains take 座 zuò, etc. Within these categories are further subdivisions—while most animals take 只 (隻) zhī, domestic animals take 头 (頭) tóu, long and flexible animals take 条 (條) tiáo, and horses take 匹 pǐ. Likewise, while long things that are flexible (such as ropes) often take 条 (條) tiáo, long things that are rigid (such as sticks) take 根 gēn, unless they are also round (like pens or cigarettes), in which case in some dialects they take 枝 zhī.^[36] Classifiers also vary in how specific they are; some (such as 朵 duǒ for flowers and other similarly clustered items) are generally only used with one type, whereas others (such as 条 (條) tiáo for long and flexible things, one-dimensional things, or abstract items like news reports)^{[note 12]} are much less restricted.^[37] Furthermore, there is not a one-to-one relationship between nouns and classifiers: the same noun may be paired with different classifiers in different situations.^[38] The specific factors that govern which classifiers are paired with which nouns have been a subject of debate among linguists.

Categories and prototypes

While mass-classifiers do not necessarily bear any semantic relationship to the noun with which they are used (e.g. box and book are not related in meaning, but one can still say "a box of books"), count-classifiers do.^[31] The precise nature of that relationship, however, is not certain, since there is so much variability in how objects may be organized and categorized by classifiers. Accounts of the semantic relationship may be grouped loosely into categorical theories, which propose that count-classifiers are matched to objects solely on the basis of inherent features of those objects (such as length or size), and prototypical theories, which propose that people learn to match a count-classifier to a specific prototypical object and to other objects that are like that prototype.^[39]

The categorical, "classical"^[40] view of classifiers was that each classifier represents a category with a set of conditions; for example, the classifier 条 (條) tiáo would represent a category defined as all objects that meet the conditions of being long, thin, and one-dimensional—and nouns using that classifier must fit all the conditions with which the category is associated. Some common semantic categories into which count-classifiers have been claimed to organize nouns include the categories of shape (long, flat, or round), size (large or small), consistency (soft or hard), animacy (human, animal, or object),^[41] and function (tools, vehicles, machines, etc.).^[42]

A mule
骡子, luózi

A donkey
驴子, lǘzi

James Tai and Wang Lianqing found that the horse classifier 匹 pǐ is sometimes used for mules and camels, but rarely for the less "horse-like" donkeys, suggesting that the choice of classifiers is influenced by prototypal closeness.^[43]

On the other hand, proponents of prototype theory propose that count-classifiers may not have innate definitions, but are associated with a noun that is prototypical of that category, and nouns that have a "family resemblance" with the prototype noun will want to use the same classifier.^{[note 13]} For example, horse in Chinese uses the classifier 匹 pǐ, as in 三匹马 (sān pǐ mǎ, "three horses")—in modern Chinese the word 匹 has no meaning. Nevertheless, nouns denoting animals that look like horses will often also use this same classifier, and native speakers have been found to be more likely to use the classifier 匹 the closer an animal looks to a horse.^[43] Furthermore, words that do not meet the "criteria" of a semantic category may still use that category because of their association with a prototype. For example, the classifier 颗 (顆) kē is used for small round items, as in 一颗子弹 (yì kē zǐdàn, "one bullet"); when words like 原子弹 (yuánzǐdàn, "atomic bomb") were later introduced into the language they also used this classifier, even though they are not small and round—therefore, their classifier must have been assigned because of the words' association with the word for bullet, which acted as a "prototype".^[44] This is an example of "generalization" from prototypes: Erbaugh has proposed that when children learn count-classifiers, they go through stages, first learning a classifier-noun pair only (such as 条鱼 tiáo yú, CL-fish), then using that classifier with multiple nouns that are similar to the prototype (such as other types of fish), then finally using that set of nouns to generalize a semantic feature associated with the classifier (such as length and flexibility) so that the classifier can then be used with new words that the person encounters.^[45]

Some classifier-noun pairings are arbitrary, or at least appear to modern speakers to have no semantic motivation.^[46] For instance, the classifier 部 bù may be used for movies and novels, but also for cars^[47] and telephones.^[48] Some of this arbitrariness may be due to what linguist James Tai refers to as "fossilization", whereby a count-classifier loses its meaning through historical changes but remains paired with some nouns. For example, the classifier 匹 pǐ used for horses is meaningless today, but in Classical Chinese may have referred to a "team of two horses",^[49] a pair of horse skeletons,^[50] or the pairing between man and horse.^{[51][note 14]} Arbitrariness may also arise when a classifier is borrowed, along with its noun, from a dialect in which it has a clear meaning to one in which it does not.^[52] In both these cases, the use of the classifier is remembered more by association with certain "prototypical" nouns (such as horse) rather than by understanding of semantic categories, and thus arbitrariness has been used as an argument in favor of the prototype theory of classifiers.^[52] Gao and Malt propose that both the category and prototype theories are correct: in their conception, some classifiers constitute "well-defined categories", others make "prototype categories", and still others are relatively arbitrary.^[53]

Neutralization

In addition to the numerous "specific" count-classifiers described above,^{[note 15]} Chinese has a "general" classifier 个 (個), pronounced gè in Mandarin.^{[note 16]} This classifier is used for people, some abstract concepts, and other words that do not have special classifiers (such as 汉堡包 hànbǎobāo "hamburger"),^[54] and may also be used as a replacement for a specific classifier such as 张 (張) zhāng or 条 (條) tiáo, especially in informal speech. In Mandarin Chinese, it has been noted as early as the 1940s that the use of 个 is increasing and that there is a general tendency towards replacing specific classifiers with it.^[55] Numerous studies have reported that both adults and children tend to use 个 when they do not know the appropriate count-classifier, and even when they do but are speaking quickly or informally.^[56] The replacement of a specific classifier with the general 个 is known as classifier neutralization^[57] ("量词个化" in Chinese, literally "classifier 个-ization"^[58]). This occurs especially often among children^[59] and aphasics (individuals with damage to language-relevant areas of the brain),^[60][61] although normal speakers also neutralize frequently. It has been reported that most speakers know the appropriate classifiers for the words they are using and believe, when asked, that those classifiers are obligatory, but nevertheless use 个 without even realizing it in actual speech.^[62] As a result, in everyday spoken Mandarin the general classifier is "hundreds of times more frequent"^[63] than the specialized ones.

Nevertheless, 个 has not completely replaced other count-classifiers, and there are still many situations in which it would be inappropriate to substitute it for the required specific classifier.^[55] There may be specific patterns behind which classifier-noun pairs may be "neutralized" to use the general classifier, and which may not. Specifically, words that are most prototypical for their categories, such as paper for the category of nouns taking the "flat/square" classifier 张 (張) zhāng, may be less likely to be said with a general classifier.^[64]

Variation in usage

A painting may be referred to with the classifiers 张 (張) zhāng and 幅 fú; both phrases have the same meaning, but convey different stylistic effects.^[65]

Depending on the classifier used, the noun 楼 lóu could be used to refer to either this building, as in 一座楼 (yí zuò lóu "one building"), or the floors of the building, as in 二十层楼 (èrshí céng lóu, "twenty floors").^[66]

It is not the case that every noun is only associated with one classifier. Across dialects and speakers there is great variability in the way classifiers are used for the same words, and speakers often do not agree which classifier is best.^[67] For example, for cars some people use 部 bù, others use 台 tái, and still others use 辆 (輛) liàng; Cantonese uses 架 gaa3. Even within a single dialect or a single speaker, the same noun may take different measure words depending on the style in which the person is speaking, or on different nuances the person wants to convey (for instance, measure words can reflect the speaker's judgment of or opinion about the object^[68]). An example of this is the word for person, 人 rén, which uses the measure word 个 (個) gè normally, but uses the measure 口 kǒu when counting number of people in a household, 位 wèi when being particularly polite or honorific, and 名 míng in formal, written contexts;^[69] likewise, a group of people may be referred to by massifiers as 一群人 (yì qún rén, "a group of people") or 一帮人 (yì bāng rén, "a gang/crowd of people"): the first is neutral, whereas the second implies that the people are unruly or otherwise being judged poorly.^[70]

Some count-classifiers may also be used with nouns that they are not normally related to, for metaphorical effect, as in 一堆烦恼 (yì duī fánnǎo, "a pile of worries/troubles").^[71] Finally, a single word may have multiple count-classifiers that convey different meanings altogether—in fact, the choice of a classifier can even influence the meaning of a noun. By way of illustration, 三节课 sān jié kè means "three class periods" (as in "I have three classes today"), whereas 三门课 sān mén kè means "three courses" (as in "I signed up for three courses this semester"), even though the noun in each sentence is the same.^[66]

Purpose

In research on classifier systems, and Chinese classifiers in particular, it has been asked why count-classifiers (as opposed to mass-classifiers) exist at all. Mass-classifiers are present in all languages since they are the only way to "count" mass nouns that are not naturally divided into units (as, for example, "three splotches of mud" in English; *"three muds" is ungrammatical). On the other hand, count-classifiers are not inherently mandatory, and are absent from most languages.^{[21][note 17]} Furthermore, count-classifiers are used with an "unexpectedly low frequency";^[72] in many settings, speakers avoid specific classifiers by just using a bare noun (without a number or demonstrative) or using the general classifier 个 gè.^[73] Linguists and typologists such as Joseph Greenberg have suggested that specific count-classifiers are semantically "redundant", repeating information present within the noun.^[74] Count-classifiers can be used stylistically, though,^[69] and can also be used to clarify or limit a speaker's intended meaning when using a vague or ambiguous noun; for example, the noun 课 kè "class" can refer to courses in a semester or specific class periods during a day, depending on whether the classifier 门 (門) mén or 节 (節) jié is used.^[75]

One proposed explanation for the existence of count-classifiers is that they serve more of a cognitive purpose than a practical one: in other words, they provide a linguistic way for speakers to organize or categorize real objects.^[76] An alternative account is that they serve more of a discursive and pragmatic function (a communicative function when people interact) rather than an abstract function within the mind.^[73] Specifically, it has been proposed that count-classifiers might be used to mark new or unfamiliar objects within a discourse,^[76] to introduce major characters or items in a story or conversation,^[77] or to foreground important information and objects by making them bigger and more salient.^[78] In this way, count-classifiers might not serve an abstract grammatical or cognitive function, but may help in communication by making important information more noticeable and drawing attention to it.

History

Classifier phrases

An oracle bone inscription from the Shāng Dynasty. Such inscriptions provide some of the earliest examples of the number phrases that may have eventually spawned Chinese classifiers.

Historical linguists have found that phrases consisting of nouns and numbers went through several structural changes in Old Chinese and Middle Chinese before classifiers appeared in them. The earliest forms may have been Number – Noun, like English (i.e. "five horses"), and the less common Noun – Number ("horses five"), both of which are attested in the oracle bone scripts of Pre-Archaic Chinese (circa 1400 BCE to 1000 BCE).^[79] The first constructions resembling classifier constructions were Noun – Number – Noun constructions, which were also extant in Pre-Archaic Chinese but less common than Number – Noun. In these constructions, sometimes the first and second nouns were identical (N1 – Number – N1, as in "horses five horses") and other times the second noun was different, but semantically related (N1 – Number – N2). According to some historical linguists, the N2 in these constructions can be considered an early form of count-classifier and has even been called an "echo classifier"; this speculation is not universally agreed on, though.^[80] Although true count-classifiers had not appeared yet, mass-classifiers were common in this time, with constructions such as "wine – six – yǒu" (the word 酉 yǒu represented a wine container) meaning "six yǒu of wine".^[80] Examples such as this suggest that mass-classifiers predate count-classifiers by several centuries, although they did not appear in the same word order as they do today.^[81]

It is from this type of structure that count-classifiers may have arisen, originally replacing the second noun (in structures where there was a noun rather than a mass-classifier) to yield Noun – Number – Classifier. That is to say, constructions like "horses five horses" may have been replaced by ones like "horses five CL", possibly for stylistic reasons such as avoiding repetition.^[82] Another reason for the appearance of count-classifiers may have been to avoid confusion or ambiguity that could have arisen from counting items using only mass-classifiers—i.e. to clarify when one is referring to a single item and when one is referring to a measure of items.^[83]

Historians agree that at some point in history the order of words in this construction shifted, putting the noun at the end rather than beginning, like in the present-day construction Number – Classifier – Noun.^[84] According to historical linguist Alain Peyraube, the earliest occurrences of this construction (albeit with mass-classifiers, rather than count-classifiers) appear in the late portion of Old Chinese (500 BCE to 200 BCE). At this time, the Number – Mass-classifier portion of the Noun – Number – Mass-classifier construction was sometimes shifted in front of the noun. Peyraube speculates that this may have occurred because it was gradually reanalyzed as a modifier (like an adjective) for the head noun, as opposed to a simple repetition as it originally was. Since Chinese generally places modifiers before modified, as does English, the shift may have been prompted by this reanalysis. By the early part of the Common Era, the nouns appearing in "classifier position" were beginning to lose their meaning and become true classifiers. Estimates of when classifiers underwent the most development vary: Wang Li claims their period of major development was during the Han Dynasty (206 BCE – 220 CE),^[85] whereas Liu Shiru estimates that it was the Southern and Northern Dynasties period (420 – 589 CE),^[86] and Peyraube chooses the Tang Dynasty (618 – 907 CE).^[87] Regardless of when they developed, Wang Lianqing claims that they did not become grammatically mandatory until sometime around the 11th century.^[88]

Classifier systems in many nearby languages and language groups (such as Vietnamese and the Tai languages) are very similar to the Chinese classifier system in both grammatical structure and the parameters along which some objects are grouped together. Thus, there has been some debate over which language family first developed classifiers and which ones then borrowed them—or whether classifier systems were native to all these languages and developed more through repeated language contact throughout history.^[89]

Classifier words

Most modern count-classifiers are derived from words that originally were free-standing nouns in older varieties of Chinese, and have since been grammaticalized to become bound morphemes.^[90] In other words, count-classifiers tend to come from words that once had specific meaning but lost it (a process known as semantic bleaching).^[91] Many, however, still have related forms that work as nouns all by themselves, such as the classifier 带 (帶) dài for long, ribbon-like objects: the modern word 带子 dàizi means "ribbon".^[71] In fact, the majority of classifiers can also be used as other parts of speech, such as nouns.^[92] Mass-classifiers, on the other hand, are more transparent in meaning than count-classifiers; while the latter have some historical meaning, the former are still full-fledged nouns. For example, 杯 (bēi, cup), is both a classifier as in 一杯茶 (yì bēi chá, "a cup of tea") and the word for a cup as in 酒杯 (jiǔbēi, "wine glass").^[93]

Where do these classifiers come from? Each classifier has its own history.

— Peyraube (1991, p. 116)

It was not always the case that every noun required a count-classifier. In many historical varieties of Chinese, use of classifiers was not mandatory, and classifiers are rare in writings that have survived.^[94] Some nouns acquired classifiers earlier than others; some of the first documented uses of classifiers were for inventorying items, both in mercantile business and in storytelling.^[95] Thus, the first nouns to have count-classifiers paired with them may have been nouns that represent "culturally valued" items such as horses, scrolls, and intellectuals.^[96] The special status of such items is still apparent today: many of the classifiers that can only be paired with one or two nouns, such as 匹 pǐ for horses^{[note 18]} and 首 shǒu for songs or poems, are the classifiers for these same "valued" items. Such classifiers make up as much as one-third of the commonly used classifiers today.^[19]

Classifiers did not gain official recognition as a lexical category (part of speech) until the 20th century. The earliest modern text to discuss classifiers and their use was Ma Jianzhong's 1898 Ma's Basic Principles for Writing Clearly (马氏文通).^[97] From then until the 1940s, linguists such as Ma, Wang Li, and Li Jinxi treated classifiers as just a type of noun that "expresses a quantity".^[85] Lü Shuxiang was the first to treat them as a separate category, calling them "unit words" (单位词 dānwèicí) in his 1940s Outline of Chinese Grammar (中国文法要略) and finally "measure words" (量词 liàngcí) in Grammar Studies (语法学习). He made this separation based on the fact that classifiers were semantically bleached, and that they can be used directly with a number, whereas true nouns need to have a measure word added before they can be used with a number.^[98] After this time, other names were also proposed for classifiers: Gao Mingkai called them "noun helper words" (助名词 zhùmíngcí), Lu Wangdao "counting markers" (计标 jìbiāo), and Japanese linguist Miyawaki Kennosuke called them "accompanying words" (陪伴词 péibàncí).^[99] In the Draft Plan for a System of Teaching Chinese Grammar [zh] adopted by the People's Republic of China in 1954, Lü's "measure words" (量词 liàngcí) was adopted as the official name for classifiers in China.^[100] This remains the most common term in use today.^[12]

General classifiers

Historically, 个 gè was not always the general classifier. Some believe it was originally a noun referring to bamboo stalks, and gradually expanded in use to become a classifier for many things with "vertical, individual, [or] upright qualit[ies]",^[101] eventually becoming a general classifier because it was used so frequently with common nouns.^[102] The classifier gè is actually associated with three different homophonous characters: 个, 個 (used today as the traditional-character equivalent of 个), and 箇. Historical linguist Lianqing Wang has argued that these characters actually originated from different words, and that only 箇 had the original meaning of "bamboo stalk".^[103] 个, he claims, was used as a general classifier early on, and may have been derived from the orthographically similar 介 jiè, one of the earliest general classifiers.^[104] 箇 later merged with 介 because they were similar in pronunciation and meaning (both used as general classifiers).^[103] Likewise, he claims that 個 was also a separate word (with a meaning having to do with "partiality" or "being a single part"), and merged with 个 for the same reasons as 箇 did; he also argues that 個 was "created", as early as the Han Dynasty, to supersede 个.^[105]

Nor was 个 the only general classifier in the history of Chinese. The aforementioned 介 jiè was being used as a general classifier before the Qin Dynasty (221 BCE); it was originally a noun referring to individual items out of a string of connected shells or clothes, and eventually came to be used as a classifier for "individual" objects (as opposed to pairs or groups of objects) before becoming a general classifier.^[106] Another general classifier was 枚 méi, which originally referred to small twigs. Since twigs were used for counting items, 枚 became a counter word: any items, including people, could be counted as "one 枚, two 枚", etc. 枚 was the most common classifier in use during the Southern and Northern Dynasties period (420–589 CE),^[107] but today is no longer a general classifier, and is only used rarely, as a specialized classifier for items such as pins and badges.^[108] Kathleen Ahrens has claimed that 隻 (zhī in Mandarin and jia in Taiwanese), the classifier for animals in Mandarin, is another general classifier in Taiwanese and may be becoming one in the Mandarin spoken in Taiwan.^[109]

Variety

Northern dialects tend to have fewer classifiers than southern ones. 個 ge is the only classifier found in the Dungan language. All nouns could have just one classifier in some dialects, such as Shanghainese (Wu), the Mandarin dialect of Shanxi, and Shandong dialects. Some dialects such as Northern Min, certain Xiang dialects, Hakka dialects, and some Yue dialects use 隻 for the noun referring to people, rather than 個.^[110]

See also

• China portal
• Languages portal

• List of Chinese classifiers
• Chinese grammar
• Collective noun
• Classifiers in other languages:
  • Burmese numerical classifiers
  • Hokkien counter word
  • Japanese counter word
  • Korean counter word
  • Vietnamese classifier

Notes

1. 
   

All examples given in this article are from standard Mandarin Chinese, with pronunciation indicated using the pinyin system, unless otherwise stated. The script would often be identical in other varieties of Chinese, although the pronunciation would vary.

Across different varieties of Chinese, classifier-noun clauses have slightly different interpretations (particularly in the interpretation of definiteness in classified nouns as opposed to bare nouns), but the requirement that a classifier come between a number and a noun is more or less the same in the major varieties (Cheng & Sybesma 2005).

Although “每” (每个人) is more generally used to mean "every person" in this case.

See, for example, similar results in the Chinese corpus of the Center for Chinese Linguistics at Peking University: 天空一片, retrieved on 3 June 2009.

In addition to the count-mass distinction and nominal-verbal distinction described below, various linguists have proposed many additional divisions of classifiers by type. He (2001, chapters 2 and 3) contains a review of these.

The Syllabus of Graded Words and Characters for Chinese Proficiency is a standardized measure of vocabulary and character recognition, used in the People's Republic of China for testing middle school students, high school students, and foreign learners. The most recent edition was published in 2003 by the Testing Center of the National Chinese Proficiency Testing Committee.

Including the following:

• Chen, Baocun 陈保存 (1988). Chinese Classifier Dictionary 汉语量词词典. Fuzhou: Fujian People's Publishing House 福建人民出版社. ISBN 978-7-211-00375-4.
• Fang, Jiqing; Connelly; Michael (2008). Chinese Measure Word Dictionary. Boston: Cheng & Tsui. ISBN 978-0-88727-632-3.
• Jiao, Fan 焦凡 (2001). A Chinese-English Dictionary of Measure Words 汉英量词词典. Beijing: Sinolingua 华语敎学出版社. ISBN 978-7-80052-568-1.
• Liu, Ziping 刘子平 (1996). Chinese Classifier Dictionary 汉语量词词典. Inner Mongolia Education Press 内蒙古教育出版社. ISBN 978-7-5311-2707-9.

Count-classifiers have also been called "individual classifiers", (Chao 1968, p. 509), "qualifying classifiers" (Zhang 2007, p. 45; Hu 1993, p. 10), and just "classifiers" (Cheng & Sybesma 1998, p. 3).

Mass-classifiers have also been called "measure words", "massifiers" (Cheng & Sybesma 1998, p. 3), "non-individual classifiers" (Chao 1968, p. 509), and "quantifying classifiers" (Zhang 2007, p. 45; Hu 1993, p. 10). The term "mass-classifier" is used in this article to avoid ambiguous usage of the term "measure word", which is often used in everyday speech to refer to both count-classifiers and mass-classifiers, even though in technical usage it only means mass-classifiers (Li 2000, p. 1116).

Also called "aggregate" (Li & Thompson 1981, pp. 107–109) or "group" (Ahrens 1994, p. 239, note 3) measures.

"Classifier phrases" are similar to noun phrases, but with a classifier rather than a noun as the head (Cheng & Sybesma 1998, pp. 16–17).

This may be because official documents during the Han Dynasty were written on long bamboo strips, making them "strips of business" (Ahrens 1994, p. 206).

The theory described in Ahrens (1994) and Wang (1994) is also referred to within those works as a "prototype" theory, but differs somewhat from the version of prototype theory described here; rather than claiming that individual prototypes are the source for classifier meanings, these authors believe that classifiers still are based on categories with features, but that the categories have many features, and "prototypes" are words that have all the features of that category whereas other words in the category only have some features. In other words, "there are core and marginal members of a category.... a member of a category does not necessarily possess all the properties of that category" (Wang 1994, p. 8). For instance, the classifier 棵 kē is used for the category of trees, which may have features such as "has a trunk", "has leaves", and "has branches", "is deciduous"; maple trees would be prototypes of the category, since they have all these features, whereas palm trees only have a trunk and leaves and thus are not prototypical (Ahrens 1994, pp. 211–12).

The apparent disagreement between the definitions provided by different authors may reflect different uses of these words in different time periods. It is well-attested that many classifiers underwent frequent changes of meaning throughout history (Wang 1994; Erbaugh 1986, pp. 426–31; Ahrens 1994, pp. 205–206), so 匹 pǐ may have had all these meanings at different points in history.

Also called "sortal classifiers" (Erbaugh 2000, p. 33; Biq 2002, p. 531).

Kathleen Ahrens claimed in 1994 that the classifier for animals—只 (隻), pronounced zhī in Mandarin and jia in Taiwanese—is in the process of becoming a second general classifier in the Mandarin spoken in Taiwan, and already is used as the general classifier in Taiwanese itself (Ahrens 1994, p. 206).

Although English does not have a productive system of count-classifiers and is not considered a "classifier language", it does have a few constructions—mostly archaic or specialized—that resemble count-classifiers, such as "X head of cattle" (T'sou 1976, p. 1221).

18. Today, 匹 may also be used for bolts of cloth. See "List of Common Nominal Measure Words" on ChineseNotes.com (last modified 11 January 2009; retrieved on 3 September 2009).

References

1. 
   

Li & Thompson 1981, p. 104

Hu 1993, p. 13

The examples are adapted from those given in Hu (1993, p. 13), Erbaugh (1986, pp. 403–404), and Li & Thompson (1981, pp. 104–105).

Zhang 2007, p. 47

Li 2000, p. 1119

Sun 2006, p. 159

Sun 2006, p. 160

Li & Thompson 1981, p. 82

Li & Thompson 1981, pp. 34–35

Li & Thompson 1981, p. 111

Hu 1993, p. 9

Li 2000, p. 1116; Hu 1993, p. 7; Wang 1994, pp. 22, 24–25; He 2001, p. 8. Also see the usage in Fang & Connelly (2008) and most introductory Chinese textbooks.

Li & Thompson 1981, p. 105

Chao 1968, section 7.9

Zhang 2007, p. 44

Erbaugh 1986, p. 403; Fang & Connelly 2008, p. ix

He 2001, p. 234

Gao & Malt 2009, p. 1133

Erbaugh 1986, p. 403

Erbaugh 1986, p. 404

Tai 1994, p. 3; Allan 1977, pp. 285–86; Wang 1994, p. 1

Ahrens 1994, p. 239, note 3

Li & Thompson 1981, p. 105; Zhang 2007, p. 44; Erbaugh 1986, p. 118, note 5

Li & Thompson 1981, pp. 105–107

Erbaugh 1986, p. 118, note 5; Hu 1993, p. 9

Erbaugh 1986, p. 118, note 5; Li & Thompson 1981, pp. 107–109

Cheng & Sybesma 1998, p. 3; Tai 1994, p. 2

Wang 1994, pp. 27–36; Cheng & Sybesma 1998

Cheng & Sybesma 1998, pp. 3–5

Wang 1994, pp. 29–30

Cheng & Sybesma 1998

Ahrens 1994, p. 239, note 5; Wang 1994, pp. 26–27, 37–48

He 2001, pp. 42, 44

Zhang 2007, p. 44; Li & Thompson 1981, p. 110; Fang & Connelly 2008, p. x

Tai 1994, p. 8

Tai 1994, pp. 7–9; Tai & Wang 1990

Erbaugh 1986, p. 111

He 2001, p. 239

Tai 1994, pp. 3–5; Ahrens 1994, pp. 208–12

Tai 1994, p. 3; Ahrens 1994, pp. 209–10

Tai 1994, p. 5; Allan 1977

Hu 1993, p. 1

Tai 1994, p. 12

Zhang 2007, pp. 46–47

Erbaugh 1986, p. 415

Hu 1993, p. 1; Tai 1994, p. 13; Zhang 2007, pp. 55–56

Zhang 2007, pp. 55–56

Gao & Malt 2009, p. 1134

Morev 2000, p. 79

Wang 1994, pp. 172–73

Tai 1994, p. 15, note 7

Tai 1994, p. 13

Gao & Malt 2009, pp. 1133–4

Hu 1993, p. 12

Tzeng, Chen & Hung 1991, p. 193

Zhang 2007, p. 57

Ahrens 1994, p. 212

He 2001, p. 165

Erbaugh 1986; Hu 1993

Ahrens 1994, pp. 227–32

Tzeng, Chen & Hung 1991

Erbaugh 1986, pp. 404–406; Ahrens 1994, pp. 202–203

Erbaugh 1986, pp. 404–406

Ahrens 1994

Zhang 2007, p. 53

Zhang 2007, p. 52

Tai 1994; Erbaugh 2000, pp. 34–35

He 2001, p. 237

Fang & Connelly 2008, p. ix; Zhang 2007, pp. 53–54

He 2001, p. 242

Shie 2003, p. 76

Erbaugh 2000, p. 34

Erbaugh 2000, pp. 425–26; Li 2000

Zhang 2007, p. 51

Zhang 2007, pp. 51–52

Erbaugh 1986, pp. 425–6

Sun 1988, p. 298

Li 2000

Peyraube 1991, p. 107; Morev 2000, pp. 78–79

Peyraube 1991, p. 108

Peyraube 1991, p. 110; Wang 1994, pp. 171–72

Morev 2000, pp. 78–79

Wang 1994, p. 172

Peyraube 1991, p. 106; Morev 2000, pp. 78–79

He 2001, p. 3

Wang 1994, pp. 2, 17

Peyraube 1991, pp. 111–17

Wang 1994, p. 3

Erbaugh 1986, p. 401; Wang 1994, p. 2

Shie 2003, p. 76; Wang 1994, pp. 113–14, 172–73

Peyraube 1991, p. 116

Gao & Malt 2009, p. 1130

Chien, Lust & Chiang 2003, p. 92

Peyraube 1991; Erbaugh 1986, p. 401

Erbaugh 1986, p. 401

Erbaugh 1986, pp. 401, 403, 428

He 2001, p. 2

He 2001, p. 4

He 2001, pp. 5–6

He 2001, p. 7

Erbaugh 1986, p. 430

Erbaugh 1986, pp. 428–30; Ahrens 1994, p. 205

Wang 1994, pp. 114–15

Wang 1994, p. 95

Wang 1994, pp. 115–16, 158

Wang 1994, pp. 93–95

Wang 1994, pp. 155–7

Erbaugh 1986, p. 428

Ahrens 1994, p. 206

110. Graham Thurgood; Randy J. LaPolla (2003). Graham Thurgood, Randy J. LaPolla (ed.). The Sino-Tibetan languages. Routledge language family. Vol. 3 (illustrated ed.). Psychology Press. p. 85. ISBN 0-7007-1129-5. Retrieved 2012-03-10. In general, the Southern dialects have a greater number of classifiers than the Northern. The farther north one travels, the smaller the variety of classifiers found. In Dunganese, a Gansu dialect of Northern Chinese spoken in Central Asia, only one classifier, 個 [kə], is used; and this same classifier has almost become the cover classifier for all nouns in Lánzhou of Gansu too. The tendency to use one general classifier for all nouns is also found to a greater or lesser extent in many Shanxi dialects, some Shandong dialects, and even the Shanghai dialect of Wu and Standard Mandarin (SM). The choice of classifiers for individual nouns is particular to each dialect. For example, although the preferred classifier across dialects for 'human being' is 個 and its cognates, 隻 in its dialect forms is widely used in the Hakka and Yue dialects of Guangxi and western Guangdong provinces as well as in the Northern Min dialects and some Xiang dialects in Hunan.

Bibliography

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External links

• List of Common Nominal Measure Words on chinesenotes.com
• Units of Weights and Measures on chinesenotes.com
• How to Use Chinese Measure Words on 3000 Hanzi

v t e Chinese language or Sinitic languages

Categories:

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Single-crystalline GeTe nanowires and nanohelices

Semiconducting GeTe nanowires (NW) and nanohelices (NH) are synthesized via vapor transport method, with metal nanoparticle catalysts. GeTe was evaporated and carried by Ar gas at optimum temperature, pressure, time, and gas flow rate to the downstream collecting/grow site (SiO₂ surface coated with colloidal gold nanoparticles). High temperature over 500 °C produces thicker nanowires and crystalline chunks. Au is essential to the growth of NW and NH and is suggested to the metal catalyst of the reaction. This method gives rise to NW and NH with a 1:1 ratio of Ge and Te. NW produced by this method average about 65 nm in diameter and up to 50 μm in length. NHs averages to 135 nm in helix diameter.^[9]

Nanocrystal (quantum size effect)

The synthesis described above has not reached the sized required to exhibit quantum size effect. Nanostructures that reach the quantum regime exhibit a different set of phenomena unseen at a larger scale, for example, spontaneous polar ordering and the splitting of diffraction spots. The synthesis of GeTe nanocrystals of average size of 8, 17, and 100 nm involves divalent Ge(II) chloride – 1,4 dioxane complex and bis[bis(trimethylsilyl)amino]Ge (II) and trioctylphosphine-tellurium in a solvent such as 1,2-dichlorobenzene or phenyl ether. Ge(II) reduction kinetics has been thought to determine the GeTe formation. Large the Ge(II) reduction rate may lead to the increase in particle nucleation rate, resulting in the reduction of particle diameter.^[10] 

https://en.wikipedia.org/wiki/Germanium_telluride#Single-crystalline_GeTe_nanowires_and_nanohelices

 

"Hymn to the Fallen" (Jiu Ge) (traditional Chinese: 國殤; simplified Chinese: 国殇; pinyin: Guó shāng; lit. 'National casualties') is a Classical Chinese poem which has been preserved in the Nine Songs (Jiu Ge) section of the ancient Chinese poetry anthology, the Chu ci, or The Songs of Chu, which is an ancient set of poems. Together, these poems constitute one of the 17 sections of the poetry anthology which was published under the title of the Chuci (also known as the Songs of Chu or as the Songs of the South). Despite the "Nine" in the title (Jiu ge literally means Nine Songs), the number of these poetic pieces actually consists of eleven separate songs, or elegies.^[1] This set of verses seems to represent some shamanistic dramatic practices of the Yangzi River valley area (as well as a northern tradition or traditions) involving the invocation of divine beings and seeking their blessings by means of a process of courtship.^[2] The poetry consists of lyrics written for performance as part of a religious drama, however the lack of stage directions or indications of who is supposed to be singing at any one time or whether some of the lines represent lines for a chorus makes an accurate reconstruction of how such a shamanic drama would actually have been performed quite uncertain; although, there are internal textual clues, for example indicating the use of spectacular costumes for the performers, and an extensive orchestra.^[3] Although not precisely dated, "Hymn to the Fallen" dates from the end of the late the Warring States period, ended 221 BCE, with possible revisions in the Han dynasty, particularly during the reign of Han Wudi, during 141 to 87 BCE . The poem has been translated into English by David Hawkes as "Hymn to the Fallen". "Guo shang" is a hymn to soldiers killed in war. Guó (國) means the "state", "kingdom", or "nation". Shāng (殤) means to "die young". Put together, the title refers to those who meet death in the course of fighting for their country. David Hawkes describes it as "surely one of the most beautiful laments for fallen soldiers in any language".^[4] 

https://en.wikipedia.org/wiki/Hymn_to_the_Fallen_(Jiu_Ge)

 

 

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In computer architecture, registers are typically addressed by mechanisms other than main memory, but may in some cases be assigned a memory address e.g. DEC PDP-10, ICT 1900.[2] Almost all computers, whether load/store architecture or not, load items of data from a larger memory into registers where they are used for arithmetic operations, bitwise operations, and other operations, and are manipulated or tested by machine instructions. Manipulated items are then often stored back to main memory, either by the same instruction or by a subsequent one. Modern processors use either static or dynamic RAM as main memory, with the latter usually accessed via one or more cache levels. Processor registers are normally at the top of the memory hierarchy, and provide the fastest way to access data. The term normally refers only to the group of registers that are directly encoded as part of an instruction, as defined by the instruction set. However, modern high-performance CPUs often have duplicates of these "architectural registers" in order to improve performance via register renaming, allowing parallel and speculative execution. Modern x86 design acquired these techniques around 1995 with the releases of Pentium Pro, Cyrix 6x86, Nx586, and AMD K5. When a computer program accesses the same data repeatedly, this is called locality of reference. Holding frequently used values in registers can be critical to a program's performance. Register allocation is performed either by a compiler in the code generation phase, or manually by an assembly language programmer. https://en.wikipedia.org/wiki/Processor_register Size Registers are normally measured by the number of bits they can hold, for example, an "8-bit register", "32-bit register", "64-bit register", or even more. In some instruction sets, the registers can operate in various modes, breaking down their storage memory into smaller parts (32-bit into four 8-bit ones, for instance) to which multiple data (vector, or one-dimensional array of data) can be loaded and operated upon at the same time. Typically it is implemented by adding extra registers that map their memory into a larger register. Processors that have the ability to execute single instructions on multiple data are called vector processors. https://en.wikipedia.org/wiki/Processor_register A geolocation-based video game or location-based video game is a type of video game where the gameplay evolves and progresses via a player's location in the world, often attained using GPS. Most location-based video games are mobile games that make use of the mobile phone's built in GPS capability, and often have real-world map integration. One of the most recognizable location-based mobile games is Pokémon Go. Location-based (GPS) games are often conflated with augmented reality (AR) games. GPS and AR are two separate technologies which are sometimes both used in a game, like in Pokémon Go and Minecraft Earth. GPS and AR functionality largely do not depend on one another but are often used in concert. A video game may be an AR game, a location-based game, both, or neither. https://en.wikipedia.org/wiki/Geolocation-based_video_game https://en.wikipedia.org/wiki/Augmented_reality https://en.wikipedia.org/wiki/Alternate_reality https://en.wikipedia.org/wiki/Multiverse https://en.wikipedia.org/wiki/Virtual_reality https://en.wikipedia.org/wiki/Simulation_hypothesis https://en.wikipedia.org/wiki/Realization_(probability) https://en.wikipedia.org/wiki/Empirical_probability Realization is the art of creating music, typically an accompaniment, from a figured bass, whether by improvisation in real time, or as a detained exercise in writing. It is most commonly associated with Baroque music. https://en.wikipedia.org/wiki/Realization_(figured_bass) Realization, also called Biographie, is a circa 35-metre (115 ft) sport climbing route on a limestone cliff on the southern face of Céüse mountain, near Gap and Sigoyer, in France. After it was first climbed in 2001 by American climber Chris Sharma, it became the first rock climb in the world to have a consensus grade of 9a+ (5.15a).[a] It is considered an historic and important route in rock climbing, and one of the most attempted climbs at its grade.[5][6] https://en.wikipedia.org/wiki/Realization_(climb) In metrology, the realisation of a unit of measure is the conversion of its definition into reality.[1] The International vocabulary of metrology identifies three distinct methods of realisation: Realisation of a measurement unit from its definition. Reproduction of measurement standards. Adopting a particular artefact as a standard. The International Bureau of Weights and Measures maintains the techniques for realisation of the base units in the International System of Units (SI).[2] https://en.wikipedia.org/wiki/Realisation_(metrology) Realized niche width is a phrase relating to ecology, is defined by the actual space that an organism inhabits and the resources it can access as a result of limiting pressures from other species (e.g. superior competitors). An organism's ecological niche is determined by the biotic and abiotic factors that make up that specific ecosystem that allow that specific organism to survive there. The width of an organism's niche is set by the range of conditions a species is able to survive in that specific environment. https://en.wikipedia.org/wiki/Realized_niche_width Realizing Increased Photosynthetic Efficiency (RIPE) is a translational research project that is genetically engineering plants to photosynthesize more efficiently to increase crop yields.[1] RIPE aims to increase agricultural production worldwide, particularly to help reduce hunger and poverty in Sub-Saharan Africa and Southeast Asia by sustainably improving the yield of key food crops including soybeans, rice, cassava[2] and cowpeas.[3] The RIPE project began in 2012, funded by a five-year, $25-million dollar grant from the Bill and Melinda Gates Foundation.[4] In 2017, the project received a $45 million-dollar reinvestment from the Gates Foundation, Foundation for Food and Agriculture Research, and the UK Government's Department for International Development.[5] In 2018, the Gates Foundation contributed an additional $13 million to accelerate the project's progress.[6] https://en.wikipedia.org/wiki/Realizing_Increased_Photosynthetic_Efficiency Realized variance or realised variance (RV, see spelling differences) is the sum of squared returns. For instance the RV can be the sum of squared daily returns for a particular month, which would yield a measure of price variation over this month. More commonly, the realized variance is computed as the sum of squared intraday returns for a particular day. The realized variance is useful because it provides a relatively accurate measure of volatility[1] which is useful for many purposes, including volatility forecasting and forecast evaluation. https://en.wikipedia.org/wiki/Realized_variance The Age of Enlightenment or the Enlightenment,[note 2] also known as the Age of Reason, was an intellectual and philosophical movement that occurred in Europe in the 17th and 18th centuries, with global influences and effects.[2][3] The Enlightenment included a range of ideas centered on the value of human happiness, the pursuit of knowledge obtained by means of reason and the evidence of the senses, and ideals such as natural law, liberty, progress, toleration, fraternity, constitutional government, and separation of church and state.[4][5] https://en.wikipedia.org/wiki/Age_of_Enlightenment https://en.wikipedia.org/wiki/Knowledge Definitions of knowledge try to determine the essential features of knowledge. Closely related terms are conception of knowledge, theory of knowledge, and analysis of knowledge. Some general features of knowledge are widely accepted among philosophers, for example, that it constitutes a cognitive success or an epistemic contact with reality and that propositional knowledge involves true belief. Most definitions of knowledge in analytic philosophy focus on propositional knowledge or knowledge-that, as in knowing that Dave is at home, in contrast to knowledge-how (know-how) expressing practical competence. However, despite the intense study of knowledge in epistemology, the disagreements about its precise nature are still both numerous and deep. Some of those disagreements arise from the fact that different theorists have different goals in mind: some try to provide a practically useful definition by delineating its most salient feature or features, while others aim at a theoretically precise definition of its necessary and sufficient conditions. Further disputes are caused by methodological differences: some theorists start from abstract and general intuitions or hypotheses, others from concrete and specific cases, and still others from linguistic usage. Additional disagreements arise concerning the standards of knowledge: whether knowledge is something rare that demands very high standards, like infallibility, or whether it is something common that requires only the possession of some evidence. One definition that many philosophers consider to be standard, and that has been discussed since ancient Greek philosophy, is justified true belief (JTB). This implies that knowledge is a mental state and that it is not possible to know something false. There is widespread agreement among analytic philosophers that knowledge is a form of true belief. The idea that justification is an additionally required component is due to the intuition that true beliefs based on superstition, lucky guesses, or erroneous reasoning do not constitute knowledge. In this regard, knowledge is more than just being right about something. The source of most disagreements regarding the nature of knowledge concerns what more is needed. According to the standard philosophical definition, it is justification. The original account understands justification internalistically as another mental state of the person, like a perceptual experience, a memory, or a second belief. This additional mental state supports the known proposition and constitutes a reason or evidence for it. However, some modern versions of the standard philosophical definition use an externalistic conception of justification instead. Many such views affirm that a belief is justified if it was produced in the right way, for example, by a reliable cognitive process. The justified-true-belief definition of knowledge came under severe criticism in the second half of the 20th century, mainly due to a series of counterexamples given by Edmund Gettier. Most of these examples aim to illustrate cases in which a justified true belief does not amount to knowledge because its justification is not relevant to its truth. This is often termed epistemic luck since it is just a fortuitous coincidence that the justified belief is also true. A few epistemologists have concluded from these counterexamples that the JTB definition of knowledge is deeply flawed and have sought a radical reconception of knowledge. However, many theorists still agree that the JTB definition is on the right track and have proposed more moderate responses to deal with the suggested counterexamples. Some hold that modifying one's conception of justification is sufficient to avoid them. Another approach is to include an additional requirement besides justification. On this view, being a justified true belief is a necessary but not a sufficient condition of knowledge. A great variety of such criteria has been suggested. They usually manage to avoid many of the known counterexamples but they often fall prey to newly proposed cases. It has been argued that, in order to circumvent all Gettier cases, the additional criterion needs to exclude epistemic luck altogether. However, this may require the stipulation of a very high standard of knowledge: that nothing less than infallibility is needed to exclude all forms of luck. The defeasibility theory of knowledge is one example of a definition based on a fourth criterion besides justified true belief. The additional requirement is that there is no truth that would constitute a defeating reason of the belief if the person knew about it. Other alternatives to the JTB definition are reliabilism, which holds that knowledge has to be produced by reliable processes, causal theories, which require that the known fact caused the knowledge, and virtue theories, which identify knowledge with the manifestation of intellectual virtues. Not all forms of knowledge are propositional, and various definitions of different forms of non-propositional knowledge have also been proposed. But among analytic philosophers this field of inquiry is less active and characterized by less controversy. Someone has practical knowledge or know-how if they possess the corresponding competence or ability. Knowledge by acquaintance constitutes a relation not to a proposition but to an object. It is defined as familiarity with its object based on direct perceptual experience of it. https://en.wikipedia.org/wiki/Definitions_of_knowledge Knowledge transfer is the sharing or disseminating of knowledge and the providing of inputs to problem solving.[1] In organizational theory, knowledge transfer is the practical problem of transferring knowledge from one part of the organization to another. Like knowledge management, knowledge transfer seeks to organize, create, capture or distribute knowledge and ensure its availability for future users. It is considered to be more than just a communication problem. If it were merely that, then a memorandum, an e-mail or a meeting would accomplish the knowledge transfer. Knowledge transfer is more complex because: knowledge resides in organizational members, tools, tasks, and their subnetworks[2] and much knowledge in organizations is tacit or hard to articulate.[3] The subject has been taken up under the title of knowledge management since the 1990s. The term has also been applied to the transfer of knowledge at the international level.[4][5] In business, knowledge transfer now has become a common topic in mergers and acquisitions.[6] It focuses on transferring technological platform, market experience, managerial expertise, corporate culture, and other intellectual capital that can improve the companies' competence.[7] Since technical skills and knowledge are very important assets for firms' competence in the global competition,[8] unsuccessful knowledge transfer can have a negative impact on corporations and lead to the expensive and time-consuming M&A not creating values to the firms.[9] https://en.wikipedia.org/wiki/Knowledge_transfer Knowledge extraction is the creation of knowledge from structured (relational databases, XML) and unstructured (text, documents, images) sources. The resulting knowledge needs to be in a machine-readable and machine-interpretable format and must represent knowledge in a manner that facilitates inferencing. Although it is methodically similar to information extraction (NLP) and ETL (data warehouse), the main criterion is that the extraction result goes beyond the creation of structured information or the transformation into a relational schema. It requires either the reuse of existing formal knowledge (reusing identifiers or ontologies) or the generation of a schema based on the source data. The RDB2RDF W3C group [1] is currently standardizing a language for extraction of resource description frameworks (RDF) from relational databases. Another popular example for knowledge extraction is the transformation of Wikipedia into structured data and also the mapping to existing knowledge (see DBpedia and Freebase). https://en.wikipedia.org/wiki/Knowledge_extraction In philosophy, a distinction is often made between two different kinds of knowledge: knowledge by acquaintance and knowledge by description. Whereas knowledge by description is something like ordinary propositional knowledge (e.g. "I know that snow is white"), knowledge by acquaintance is familiarity with a person, place, or thing, typically obtained through perceptual experience (e.g. "I know Sam", "I know the city of Bogotá", or "I know Russell's Problems of Philosophy").[1] According to Bertrand Russell's classic account of acquaintance knowledge, acquaintance is a direct causal interaction between a person and some object that the person is perceiving. https://en.wikipedia.org/wiki/Knowledge_by_acquaintance The knowledge economy (or the knowledge-based economy) is an economic system in which the production of goods and services is based principally on knowledge-intensive activities that contribute to advancement in technical and scientific innovation.[1] The key element of value is the greater dependence on human capital and intellectual property for the source of the innovative ideas, information and practices.[2] Organisations are required to capitalise this "knowledge" into their production to stimulate and deepen the business development process. There is less reliance on physical input and natural resources. A knowledge-based economy relies on the crucial role of intangible assets within the organisations' settings in facilitating modern economic growth.[3] https://en.wikipedia.org/wiki/Knowledge_economy The knowledge argument (also known as Mary's Room or Mary the super-scientist) is a philosophical thought experiment proposed by Frank Jackson in his article "Epiphenomenal Qualia" (1982) and extended in "What Mary Didn't Know" (1986). The experiment describes Mary, a scientist who exists in a black-and-white world where she has extensive access to physical descriptions of color, but no actual perceptual experience of color. Mary has learned everything there is to learn about color, but she has never actually experienced it for herself. The central question of the thought experiment is whether Mary will gain new knowledge when she goes outside the colorless world and experiences seeing in color https://en.wikipedia.org/wiki/Knowledge_argument Knowledge management (KM) is the collection of methods relating to creating, sharing, using and managing the knowledge and information of an organization.[1] It refers to a multidisciplinary approach to achieve organizational objectives by making the best use of knowledge.[2] https://en.wikipedia.org/wiki/Knowledge_management Embedding of a knowledge graph. The vector representation of the entities and relations can be used for different machine learning applications. In representation learning, knowledge graph embedding (KGE), also referred to as knowledge representation learning (KRL), or multi-relation learning,[1] is a machine learning task of learning a low-dimensional representation of a knowledge graph's entities and relations while preserving their semantic meaning.[1][2][3] Leveraging their embedded representation, knowledge graphs (KGs) can be used for various applications such as link prediction, triple classification, entity recognition, clustering, and relation extraction.[1][4] https://en.wikipedia.org/wiki/Knowledge_graph_embedding A relationship extraction task requires the detection and classification of semantic relationship mentions within a set of artifacts, typically from text or XML documents. The task is very similar to that of information extraction (IE), but IE additionally requires the removal of repeated relations (disambiguation) and generally refers to the extraction of many different relationships. https://en.wikipedia.org/wiki/Relationship_extraction A document is a written, drawn, presented, or memorialized representation of thought, often the manifestation of non-fictional, as well as fictional, content. The word originates from the Latin Documentum, which denotes a "teaching" or "lesson": the verb doceō denotes "to teach". In the past, the word was usually used to denote written proof useful as evidence of a truth or fact. In the Computer Age, "document" usually denotes a primarily textual computer file, including its structure and format, e.g. fonts, colors, and images. Contemporarily, "document" is not defined by its transmission medium, e.g., paper, given the existence of electronic documents. "Documentation" is distinct because it has more denotations than "document". Documents are also distinguished from "realia", which are three-dimensional objects that would otherwise satisfy the definition of "document" because they memorialize or represent thought; documents are considered more as 2-dimensional representations. While documents can have large varieties of customization, all documents can be shared freely and have the right to do so, creativity can be represented by documents, also. History, events, examples, opinions, etc. all can be expressed in documents. https://en.wikipedia.org/wiki/Document In library classification systems, realia are three-dimensional objects from real life such as coins, tools, and textiles, that do not fit into the traditional categories of library material. They can be either man-made (artifacts, tools, utensils, etc.) or naturally occurring (specimens, samples, etc.), usually borrowed, purchased, or received as donation by a teacher, library, or museum for use in classroom instruction or in exhibits. Archival and manuscript collections often receive items of memorabilia such as badges, emblems, insignias, jewelry, leather goods, needlework, etc., in connection with gifts of personal papers. Most government or institutional archives reject gifts of non-documentary objects unless they have a documentary value. When accepting large bequests of mixed objects they normally have the donors sign legal documents giving permission to the archive to destroy, exchange, sell, or dispose in any way those objects which, according to the best judgement of the archivist, are not manuscripts (which can include typescripts or printouts) or are not immediately useful for understanding the manuscripts. Recently, the usage of this term has been criticized by librarians based on the usage of term realia to refer to artistic and historical artifacts and objects, and suggesting the use of the phrase "real world object" to describe the broader categories of three-dimensional objects in libraries. https://en.wikipedia.org/wiki/Realia_(library_science) https://en.wikipedia.org/wiki/Knowledge_Web https://en.wikipedia.org/wiki/Commonsense_knowledge_(artificial_intelligence) https://en.wikipedia.org/wiki/Zero_knowledge https://en.wikipedia.org/wiki/Knowledge_Network https://en.wikipedia.org/wiki/Tacit_knowledge https://en.wikipedia.org/wiki/Procedural_knowledge https://en.wikipedia.org/wiki/The_Archaeology_of_Knowledge https://en.wikipedia.org/wiki/Knowledge_distillation https://en.wikipedia.org/wiki/Definitions_of_knowledge https://en.wikipedia.org/wiki/Knowledge_representation_and_reasoning https://en.wikipedia.org/wiki/Divine_knowledge https://en.wikipedia.org/wiki/Curse_of_knowledge https://en.wikipedia.org/wiki/Decolonization_of_knowledge https://en.wikipedia.org/wiki/Science https://en.wikipedia.org/wiki/Word_of_Knowledge https://en.wikipedia.org/wiki/Knowledge_base https://en.wikipedia.org/wiki/Encyclopedia https://en.wikipedia.org/wiki/Desacralization_of_knowledge https://en.wikipedia.org/wiki/Meta-knowledge https://en.wikipedia.org/wiki/Metacognition#Metastrategic_knowledge https://en.wikipedia.org/wiki/Core_Knowledge_Foundation https://en.wikipedia.org/wiki/Western_esotericism https://en.wikipedia.org/wiki/Dangerous_Knowledge https://en.wikipedia.org/wiki/Coloniality_of_knowledge https://en.wikipedia.org/wiki/Gettier_problem https://en.wikipedia.org/wiki/Artificial_intelligence#Knowledge_representation https://en.wikipedia.org/wiki/Ontology_language#Classification_of_ontology_languages https://en.wikipedia.org/wiki/Academic_discipline https://en.wikipedia.org/wiki/Forbidden_fruit https://en.wikipedia.org/wiki/Knowledge,_Skills,_and_Abilities https://en.wikipedia.org/wiki/Knowledge_Navigator https://en.wikipedia.org/wiki/Knowledge_and_Its_Limits https://en.wikipedia.org/wiki/Monopolies_of_knowledge https://en.wikipedia.org/wiki/Knowledge_(legal_construct) https://en.wikipedia.org/wiki/Empirical_evidence https://en.wikipedia.org/wiki/Self-knowledge https://en.wikipedia.org/wiki/Tree_of_the_knowledge_of_good_and_evil https://en.wikipedia.org/wiki/Knowledge_acquisition https://en.wikipedia.org/wiki/Open_knowledge https://en.wikipedia.org/wiki/Book_of_Knowledge https://en.wikipedia.org/wiki/Taxes_on_knowledge https://en.wikipedia.org/wiki/General_knowledge https://en.wikipedia.org/wiki/Zero-knowledge_proof From Wikipedia, the free encyclopedia "ZKP" redirects here. For the airport in Russia, see Zyryanka Airport. For other uses, see Zero knowledge. In cryptography, a zero-knowledge proof or zero-knowledge protocol is a method by which one party (the prover) can prove to another party (the verifier) that a given statement is true while the prover avoids conveying any additional information apart from the fact that the statement is indeed true. The essence of zero-knowledge proofs is that it is trivial to prove that one possesses knowledge of certain information by simply revealing it; the challenge is to prove such possession without revealing the information itself or any additional information.[1] If proving a statement requires that the prover possess some secret information, then the verifier will not be able to prove the statement to anyone else without possessing the secret information. The statement being proved must include the assertion that the prover has such knowledge, but without including or transmitting the knowledge itself in the assertion. Otherwise, the statement would not be proved in zero-knowledge because it provides the verifier with additional information about the statement by the end of the protocol. A zero-knowledge proof of knowledge is a special case when the statement consists only of the fact that the prover possesses the secret information. Interactive zero-knowledge proofs require interaction between the individual (or computer system) proving their knowledge and the individual validating the proof.[1] This section needs to be updated. The reason given is: There are also Non-interactive zero-knowledge proofs. Please help update this article to reflect recent events or newly available information. (December 2022) A protocol implementing zero-knowledge proofs of knowledge must necessarily require interactive input from the verifier. This interactive input is usually in the form of one or more challenges such that the responses from the prover will convince the verifier if and only if the statement is true, i.e., if the prover does possess the claimed knowledge. If this were not the case, the verifier could record the execution of the protocol and replay it to convince someone else that they possess the secret information. The new party's acceptance is either justified since the replayer does possess the information (which implies that the protocol leaked information, and thus, is not proved in zero-knowledge), or the acceptance is spurious, i.e., was accepted from someone who does not actually possess the information. Some forms of non-interactive zero-knowledge proofs exist,[2][3] but the validity of the proof relies on computational assumptions (typically the assumptions of an ideal cryptographic hash function). Abstract examples The Ali Baba cave Peggy randomly takes either path A or B, while Victor waits outside Victor chooses an exit path Peggy reliably appears at the exit Victor names There is a well-known story presenting the fundamental ideas of zero-knowledge proofs, first published in 1990 by Jean-Jacques Quisquater and others in their paper "How to Explain Zero-Knowledge Protocols to Your Children".[4] Using the common Alice and Bob anthropomorphic thought experiment placeholders, the two parties in a zero-knowledge proof are Peggy as the prover of the statement, and Victor, the verifier of the statement. In this story, Peggy has uncovered the secret word used to open a magic door in a cave. The cave is shaped like a ring, with the entrance on one side and the magic door blocking the opposite side. Victor wants to know whether Peggy knows the secret word; but Peggy, being a very private person, does not want to reveal her knowledge (the secret word) to Victor or to reveal the fact of her knowledge to the world in general. They label the left and right paths from the entrance A and B. First, Victor waits outside the cave as Peggy goes in. Peggy takes either path A or B; Victor is not allowed to see which path she takes. Then, Victor enters the cave and shouts the name of the path he wants her to use to return, either A or B, chosen at random. Providing she really does know the magic word, this is easy: she opens the door, if necessary, and returns along the desired path. However, suppose she did not know the word. Then, she would only be able to return by the named path if Victor were to give the name of the same path by which she had entered. Since Victor would choose A or B at random, she would have a 50% chance of guessing correctly. If they were to repeat this trick many times, say 20 times in a row, her chance of successfully anticipating all of Victor's requests would become very small (1 in 220, or very roughly 1 in a million). Thus, if Peggy repeatedly appears at the exit Victor names, he can conclude that it is extremely probable that Peggy does, in fact, know the secret word. One side note with respect to third-party observers: even if Victor is wearing a hidden camera that records the whole transaction, the only thing the camera will record is in one case Victor shouting "A!" and Peggy appearing at A or in the other case Victor shouting "B!" and Peggy appearing at B. A recording of this type would be trivial for any two people to fake (requiring only that Peggy and Victor agree beforehand on the sequence of A's and B's that Victor will shout). Such a recording will certainly never be convincing to anyone but the original participants. In fact, even a person who was present as an observer at the original experiment would be unconvinced, since Victor and Peggy might have orchestrated the whole "experiment" from start to finish. Further notice that if Victor chooses his A's and B's by flipping a coin on-camera, this protocol loses its zero-knowledge property; the on-camera coin flip would probably be convincing to any person watching the recording later. Thus, although this does not reveal the secret word to Victor, it does make it possible for Victor to convince the world in general that Peggy has that knowledge—counter to Peggy's stated wishes. However, digital cryptography generally "flips coins" by relying on a pseudo-random number generator, which is akin to a coin with a fixed pattern of heads and tails known only to the coin's owner. If Victor's coin behaved this way, then again it would be possible for Victor and Peggy to have faked the "experiment", so using a pseudo-random number generator would not reveal Peggy's knowledge to the world in the same way that using a flipped coin would. Notice that Peggy could prove to Victor that she knows the magic word, without revealing it to him, in a single trial. If both Victor and Peggy go together to the mouth of the cave, Victor can watch Peggy go in through A and come out through B. This would prove with certainty that Peggy knows the magic word, without revealing the magic word to Victor. However, such a proof could be observed by a third party, or recorded by Victor and such a proof would be convincing to anybody. In other words, Peggy could not refute such proof by claiming she colluded with Victor, and she is therefore no longer in control of who is aware of her knowledge. Two balls and the colour-blind friend Imagine your friend "Victor" is red-green colour-blind (while you are not) and you have two balls: one red and one green, but otherwise identical. To Victor, the balls seem completely identical. Victor is skeptical that the balls are actually distinguishable. You want to prove to Victor that the balls are in fact differently-coloured, but nothing else. In particular, you do not want to reveal which ball is the red one and which is the green. Here is the proof system. You give the two balls to Victor and he puts them behind his back. Next, he takes one of the balls and brings it out from behind his back and displays it. He then places it behind his back again and then chooses to reveal just one of the two balls, picking one of the two at random with equal probability. He will ask you, "Did I switch the ball?" This whole procedure is then repeated as often as necessary. By looking at the balls' colours, you can, of course, say with certainty whether or not he switched them. On the other hand, if the balls were the same colour and hence indistinguishable, there is no way you could guess correctly with probability higher than 50%. Since the probability that you would have randomly succeeded at identifying each switch/non-switch is 50%, the probability of having randomly succeeded at all switch/non-switches approaches zero ("soundness"). If you and your friend repeat this "proof" multiple times (e.g. 20 times), your friend should become convinced ("completeness") that the balls are indeed differently coloured. The above proof is zero-knowledge because your friend never learns which ball is green and which is red; indeed, he gains no knowledge about how to distinguish the balls.[5] Definition This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources in this section. Unsourced material may be challenged and removed. Find sources: "Zero-knowledge proof" – news · newspapers · books · scholar · JSTOR (July 2022) (Learn how and when to remove this template message) A zero-knowledge proof of some statement must satisfy three properties: Completeness: if the statement is true, an honest verifier (that is, one following the protocol properly) will be convinced of this fact by an honest prover. Soundness: if the statement is false, no cheating prover can convince an honest verifier that it is true, except with some small probability. Zero-knowledge: if the statement is true, no verifier learns anything other than the fact that the statement is true. In other words, just knowing the statement (not the secret) is sufficient to imagine a scenario showing that the prover knows the secret. This is formalized by showing that every verifier has some simulator that, given only the statement to be proved (and no access to the prover), can produce a transcript that "looks like" an interaction between an honest prover and the verifier in question. The first two of these are properties of more general interactive proof systems. The third is what makes the proof zero-knowledge.[6] Zero-knowledge proofs are not proofs in the mathematical sense of the term because there is some small probability, the soundness error, that a cheating prover will be able to convince the verifier of a false statement. In other words, zero-knowledge proofs are probabilistic "proofs" rather than deterministic proofs. However, there are techniques to decrease the soundness error to negligibly small values (e.g. guessing correctly on a hundred or thousand binary decisions has a 1 / 2^100 or 1/ 2^1000 soundness error, respectively. As the number of bits increases, soundness error decreases toward zero). A formal definition of zero-knowledge has to use some computational model, the most common one being that of a Turing machine. Let P P, V V, and S S be Turing machines. An interactive proof system with ( P , V ) {\displaystyle (P,V)} for a language L L is zero-knowledge if for any probabilistic polynomial time (PPT) verifier V ^ {\hat {V}} there exists a PPT simulator S S such that ∀ x ∈ L , z ∈ { 0 , 1 } ∗ , View V ^ ⁡ [ P ( x ) ↔ V ^ ( x , z ) ] = S ( x , z ) {\displaystyle \forall x\in L,z\in \{0,1\}^{*},\operatorname {View} _{\hat {V}}\left[P(x)\leftrightarrow {\hat {V}}(x,z)\right]=S(x,z)} where View V ^ ⁡ [ P ( x ) ↔ V ^ ( x , z ) ] {\displaystyle \operatorname {View} _{\hat {V}}\left[P(x)\leftrightarrow {\hat {V}}(x,z)\right]} is a record of the interactions between P ( x ) P(x) and V ^ ( x , z ) {\displaystyle {\hat {V}}(x,z)}. The prover P P is modeled as having unlimited computation power (in practice, P P usually is a probabilistic Turing machine). Intuitively, the definition states that an interactive proof system ( P , V ) {\displaystyle (P,V)} is zero-knowledge if for any verifier V ^ {\hat {V}} there exists an efficient simulator S S (depending on V ^ {\hat {V}}) that can reproduce the conversation between P P and V ^ {\hat {V}} on any given input. The auxiliary string z z in the definition plays the role of "prior knowledge" (including the random coins of V ^ {\hat {V}}). The definition implies that V ^ {\hat {V}} cannot use any prior knowledge string z z to mine information out of its conversation with P P, because if S S is also given this prior knowledge then it can reproduce the conversation between V ^ {\hat {V}} and P P just as before.[citation needed] The definition given is that of perfect zero-knowledge. Computational zero-knowledge is obtained by requiring that the views of the verifier V ^ {\hat {V}} and the simulator are only computationally indistinguishable, given the auxiliary string.[citation needed] Practical examples Discrete log of a given value We can apply these ideas to a more realistic cryptography application. Peggy wants to prove to Victor that she knows the discrete log of a given value in a given group.[7] For example, given a value y y, a large prime p p and a generator g g, she wants to prove that she knows a value x x such that g x mod p = y {\displaystyle g^{x}{\bmod {p}}=y}, without revealing x x. Indeed, knowledge of x x could be used as a proof of identity, in that Peggy could have such knowledge because she chose a random value x x that she didn't reveal to anyone, computed y = g x mod p {\displaystyle y=g^{x}{\bmod {p}}} and distributed the value of y y to all potential verifiers, such that at a later time, proving knowledge of x x is equivalent to proving identity as Peggy. The protocol proceeds as follows: in each round, Peggy generates a random number r r, computes C = g r mod p {\displaystyle C=g^{r}{\bmod {p}}} and discloses this to Victor. After receiving C C, Victor randomly issues one of the following two requests: he either requests that Peggy discloses the value of r r, or the value of ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}}. With either answer, Peggy is only disclosing a random value, so no information is disclosed by a correct execution of one round of the protocol. Victor can verify either answer; if he requested r r, he can then compute g r mod p {\displaystyle g^{r}{\bmod {p}}} and verify that it matches C C. If he requested ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}}, he can verify that C C is consistent with this, by computing g ( x + r ) mod ( p − 1 ) mod p {\displaystyle g^{(x+r){\bmod {(p-1)}}}{\bmod {p}}} and verifying that it matches ( C ⋅ y ) mod p {\displaystyle (C\cdot y){\bmod {p}}}. If Peggy indeed knows the value of x x, she can respond to either one of Victor's possible challenges. If Peggy knew or could guess which challenge Victor is going to issue, then she could easily cheat and convince Victor that she knows x x when she does not: if she knows that Victor is going to request r r, then she proceeds normally: she picks r r, computes C = g r mod p {\displaystyle C=g^{r}{\bmod {p}}} and discloses C C to Victor; she will be able to respond to Victor's challenge. On the other hand, if she knows that Victor will request ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}}, then she picks a random value r ′ r', computes C ′ = g r ′ ⋅ ( g x ) − 1 mod p {\displaystyle C'=g^{r'}\cdot \left(g^{x}\right)^{-1}{\bmod {p}}}, and discloses C ′ C' to Victor as the value of C C that he is expecting. When Victor challenges her to reveal ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}}, she reveals r ′ r', for which Victor will verify consistency, since he will in turn compute g r ′ mod p {\displaystyle g^{r'}{\bmod {p}}}, which matches C ′ ⋅ y C'\cdot y, since Peggy multiplied by the modular multiplicative inverse of y y. However, if in either one of the above scenarios Victor issues a challenge other than the one she was expecting and for which she manufactured the result, then she will be unable to respond to the challenge under the assumption of infeasibility of solving the discrete log for this group. If she picked r r and disclosed C = g r mod p {\displaystyle C=g^{r}{\bmod {p}}}, then she will be unable to produce a valid ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}} that would pass Victor's verification, given that she does not know x x. And if she picked a value r ′ r' that poses as ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}}, then she would have to respond with the discrete log of the value that she disclosed – but Peggy does not know this discrete log, since the value C she disclosed was obtained through arithmetic with known values, and not by computing a power with a known exponent. Thus, a cheating prover has a 0.5 probability of successfully cheating in one round. By executing a large enough number of rounds, the probability of a cheating prover succeeding can be made arbitrarily low. Short summary Peggy proves to know the value of x (for example her password). Peggy and Victor agree on a prime p p and a generator g g of the multiplicative group of the field Z p {\displaystyle \mathbb {Z} _{p}}. Peggy calculates the value y = g x mod p {\displaystyle y=g^{x}{\bmod {p}}} and transfers the value to Victor. The following two steps are repeated a (large) number of times. Peggy repeatedly picks a random value r ∈ U [ 0 , p − 2 ] {\displaystyle r\in U[0,p-2]} and calculates C = g r mod p {\displaystyle C=g^{r}{\bmod {p}}}. She transfers the value C C to Victor. Victor asks Peggy to calculate and transfer either the value ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(p-1)}}} or the value r r. In the first case Victor verifies ( C ⋅ y ) mod p ≡ g ( x + r ) mod ( p − 1 ) mod p {\displaystyle (C\cdot y){\bmod {p}}\equiv g^{(x+r){\bmod {(p-1)}}}{\bmod {p}}}. In the second case he verifies C ≡ g r mod p {\displaystyle C\equiv g^{r}{\bmod {p}}}. The value ( x + r ) mod ( p − 1 ) {\displaystyle (x+r){\bmod {(}}p-1)} can be seen as the encrypted value of x mod ( p − 1 ) {\displaystyle x{\bmod {(}}p-1)}. If r r is truly random, equally distributed between zero and ( p − 2 ) {\displaystyle (p-2)}, this does not leak any information about x x (see one-time pad). Hamiltonian cycle for a large graph The following scheme is due to Manuel Blum.[8] In this scenario, Peggy knows a Hamiltonian cycle for a large graph G. Victor knows G but not the cycle (e.g., Peggy has generated G and revealed it to him.) Finding a Hamiltonian cycle given a large graph is believed to be computationally infeasible, since its corresponding decision version is known to be NP-complete. Peggy will prove that she knows the cycle without simply revealing it (perhaps Victor is interested in buying it but wants verification first, or maybe Peggy is the only one who knows this information and is proving her identity to Victor). To show that Peggy knows this Hamiltonian cycle, she and Victor play several rounds of a game. At the beginning of each round, Peggy creates H, a graph which is isomorphic to G (i.e. H is just like G except that all the vertices have different names). Since it is trivial to translate a Hamiltonian cycle between isomorphic graphs with known isomorphism, if Peggy knows a Hamiltonian cycle for G she also must know one for H. Peggy commits to H. She could do so by using a cryptographic commitment scheme. Alternatively, she could number the vertices of H. Next, for each edge of H, on a small piece of paper, she writes down the two vertices that the edge joins. Then she puts all these pieces of paper face down on a table. The purpose of this commitment is that Peggy is not able to change H while, at the same time, Victor has no information about H. Victor then randomly chooses one of two questions to ask Peggy. He can either ask her to show the isomorphism between H and G (see graph isomorphism problem), or he can ask her to show a Hamiltonian cycle in H. If Peggy is asked to show that the two graphs are isomorphic, she first uncovers all of H (e.g. by turning over all pieces of papers that she put on the table) and then provides the vertex translations that map G to H. Victor can verify that they are indeed isomorphic. If Peggy is asked to prove that she knows a Hamiltonian cycle in H, she translates her Hamiltonian cycle in G onto H and only uncovers the edges on the Hamiltonian cycle. This is enough for Victor to check that H does indeed contain a Hamiltonian cycle. It is important that the commitment to the graph be such that Victor can verify, in the second case, that the cycle is really made of edges from H. This can be done by, for example, committing to every edge (or lack thereof) separately. Completeness If Peggy does know a Hamiltonian cycle in G, she can easily satisfy Victor's demand for either the graph isomorphism producing H from G (which she had committed to in the first step) or a Hamiltonian cycle in H (which she can construct by applying the isomorphism to the cycle in G). Zero-knowledge Peggy's answers do not reveal the original Hamiltonian cycle in G. Each round, Victor will learn only H's isomorphism to G or a Hamiltonian cycle in H. He would need both answers for a single H to discover the cycle in G, so the information remains unknown as long as Peggy can generate a distinct H every round. If Peggy does not know of a Hamiltonian cycle in G, but somehow knew in advance what Victor would ask to see each round then she could cheat. For example, if Peggy knew ahead of time that Victor would ask to see the Hamiltonian cycle in H then she could generate a Hamiltonian cycle for an unrelated graph. Similarly, if Peggy knew in advance that Victor would ask to see the isomorphism then she could simply generate an isomorphic graph H (in which she also does not know a Hamiltonian cycle). Victor could simulate the protocol by himself (without Peggy) because he knows what he will ask to see. Therefore, Victor gains no information about the Hamiltonian cycle in G from the information revealed in each round. Soundness If Peggy does not know the information, she can guess which question Victor will ask and generate either a graph isomorphic to G or a Hamiltonian cycle for an unrelated graph, but since she does not know a Hamiltonian cycle for G she cannot do both. With this guesswork, her chance of fooling Victor is 2−n, where n is the number of rounds. For all realistic purposes, it is infeasibly difficult to defeat a zero-knowledge proof with a reasonable number of rounds in this way. Variants of zero-knowledge Different variants of zero-knowledge can be defined by formalizing the intuitive concept of what is meant by the output of the simulator "looking like" the execution of the real proof protocol in the following ways: We speak of perfect zero-knowledge if the distributions produced by the simulator and the proof protocol are distributed exactly the same. This is for instance the case in the first example above. Statistical zero-knowledge[9] means that the distributions are not necessarily exactly the same, but they are statistically close, meaning that their statistical difference is a negligible function. We speak of computational zero-knowledge if no efficient algorithm can distinguish the two distributions. Zero knowledge types Proof of knowledge: the knowledge is hidden in the exponent like in the example shown above. Pairing based cryptography: given f(x) and f(y), without knowing x and y, it is possible to compute f(x×y). Witness indistinguishable proof: verifiers cannot know which witness is used for producing the proof. Multi-party computation: while each party can keep their respective secret, they together produce a result. Ring signature: outsiders have no idea which key is used for signing. Applications Authentication systems Research in zero-knowledge proofs has been motivated by authentication systems where one party wants to prove its identity to a second party via some secret information (such as a password) but doesn't want the second party to learn anything about this secret. This is called a "zero-knowledge proof of knowledge". However, a password is typically too small or insufficiently random to be used in many schemes for zero-knowledge proofs of knowledge. A zero-knowledge password proof is a special kind of zero-knowledge proof of knowledge that addresses the limited size of passwords.[citation needed] In April 2015, the Sigma protocol (one-out-of-many proofs) was introduced.[10] In August 2021, Cloudflare, an American web infrastructure and security company decided to use the one-out-of-many proofs mechanism for private web verification using vendor hardware.[11] Ethical behavior One of the uses of zero-knowledge proofs within cryptographic protocols is to enforce honest behavior while maintaining privacy. Roughly, the idea is to force a user to prove, using a zero-knowledge proof, that its behavior is correct according to the protocol.[12][13] Because of soundness, we know that the user must really act honestly in order to be able to provide a valid proof. Because of zero knowledge, we know that the user does not compromise the privacy of its secrets in the process of providing the proof.[citation needed] Nuclear disarmament In 2016, the Princeton Plasma Physics Laboratory and Princeton University demonstrated a technique that may have applicability to future nuclear disarmament talks. It would allow inspectors to confirm whether or not an object is indeed a nuclear weapon without recording, sharing or revealing the internal workings which might be secret.[14] Blockchains Zero-knowledge proofs were applied in the Zerocoin and Zerocash protocols, which culminated in the birth of Zcoin[15] (later rebranded as Firo in 2020)[16] and Zcash cryptocurrencies in 2016. Zerocoin has a built-in mixing model that does not trust any peers or centralised mixing providers to ensure anonymity.[15] Users can transact in a base currency and can cycle the currency into and out of Zerocoins.[17] The Zerocash protocol uses a similar model (a variant known as a non-interactive zero-knowledge proof)[18] except that it can obscure the transaction amount, while Zerocoin cannot. Given significant restrictions of transaction data on the Zerocash network, Zerocash is less prone to privacy timing attacks when compared to Zerocoin. However, this additional layer of privacy can cause potentially undetected hyperinflation of Zerocash supply because fraudulent coins cannot be tracked.[15][19] In 2018, Bulletproofs were introduced. Bulletproofs are an improvement from non-interactive zero-knowledge proof where trusted setup is not needed.[20] It was later implemented into the Mimblewimble protocol (which the Grin and Beam cryptocurrencies are based upon) and Monero cryptocurrency.[21] In 2019, Firo implemented the Sigma protocol, which is an improvement on the Zerocoin protocol without trusted setup.[22][10] In the same year, Firo introduced the Lelantus protocol, an improvement on the Sigma protocol, where the former hides the origin and amount of a transaction.[23] History Zero-knowledge proofs were first conceived in 1985 by Shafi Goldwasser, Silvio Micali, and Charles Rackoff in their paper "The Knowledge Complexity of Interactive Proof-Systems".[12] This paper introduced the IP hierarchy of interactive proof systems (see interactive proof system) and conceived the concept of knowledge complexity, a measurement of the amount of knowledge about the proof transferred from the prover to the verifier. They also gave the first zero-knowledge proof for a concrete problem, that of deciding quadratic nonresidues mod m. Together with a paper by László Babai and Shlomo Moran, this landmark paper invented interactive proof systems, for which all five authors won the first Gödel Prize in 1993. In their own words, Goldwasser, Micali, and Rackoff say: Of particular interest is the case where this additional knowledge is essentially 0 and we show that [it] is possible to interactively prove that a number is quadratic non residue mod m releasing 0 additional knowledge. This is surprising as no efficient algorithm for deciding quadratic residuosity mod m is known when m’s factorization is not given. Moreover, all known NP proofs for this problem exhibit the prime factorization of m. This indicates that adding interaction to the proving process, may decrease the amount of knowledge that must be communicated in order to prove a theorem. The quadratic nonresidue problem has both an NP and a co-NP algorithm, and so lies in the intersection of NP and co-NP. This was also true of several other problems for which zero-knowledge proofs were subsequently discovered, such as an unpublished proof system by Oded Goldreich verifying that a two-prime modulus is not a Blum integer.[24] Oded Goldreich, Silvio Micali, and Avi Wigderson took this one step further, showing that, assuming the existence of unbreakable encryption, one can create a zero-knowledge proof system for the NP-complete graph coloring problem with three colors. Since every problem in NP can be efficiently reduced to this problem, this means that, under this assumption, all problems in NP have zero-knowledge proofs.[25] The reason for the assumption is that, as in the above example, their protocols require encryption. A commonly cited sufficient condition for the existence of unbreakable encryption is the existence of one-way functions, but it is conceivable that some physical means might also achieve it. On top of this, they also showed that the graph nonisomorphism problem, the complement of the graph isomorphism problem, has a zero-knowledge proof. This problem is in co-NP, but is not currently known to be in either NP or any practical class. More generally, Russell Impagliazzo and Moti Yung as well as Ben-Or et al. would go on to show that, also assuming one-way functions or unbreakable encryption, that there are zero-knowledge proofs for all problems in IP = PSPACE, or in other words, anything that can be proved by an interactive proof system can be proved with zero knowledge.[26][27] Not liking to make unnecessary assumptions, many theorists sought a way to eliminate the necessity of one way functions. One way this was done was with multi-prover interactive proof systems (see interactive proof system), which have multiple independent provers instead of only one, allowing the verifier to "cross-examine" the provers in isolation to avoid being misled. It can be shown that, without any intractability assumptions, all languages in NP have zero-knowledge proofs in such a system.[28] It turns out that in an Internet-like setting, where multiple protocols may be executed concurrently, building zero-knowledge proofs is more challenging. The line of research investigating concurrent zero-knowledge proofs was initiated by the work of Dwork, Naor, and Sahai.[29] One particular development along these lines has been the development of witness-indistinguishable proof protocols. The property of witness-indistinguishability is related to that of zero-knowledge, yet witness-indistinguishable protocols do not suffer from the same problems of concurrent execution.[30] Another variant of zero-knowledge proofs are non-interactive zero-knowledge proofs. Blum, Feldman, and Micali showed that a common random string shared between the prover and the verifier is enough to achieve computational zero-knowledge without requiring interaction.[2][3] Zero-Knowledge Proof protocols The most popular interactive or non-interactive zero-knowledge proof (e.g., zk-SNARK) protocols can be broadly categorized in the following four categories: Succinct Non-Interactive ARguments of Knowledge (SNARK), Scalable Transparent ARgument of Knowledge (STARK), Verifiable Polynomial Delegation (VPD), and Succinct Non-interactive ARGuments (SNARG). A list of zero-knowledge proof protocols and libraries is provided below along with comparisons based on transparency, universality, plausible post-quantum security, and programming paradigm.[31] A transparent protocol is one that does not require any trusted setup and uses public randomness. A universal protocol is one that does not require a separate trusted setup for each circuit. Finally, a plausibly post-quantum protocol is one that is not susceptible to known attacks involving quantum algorithms. Zero-knowledge proof (ZKP) systems ZKP System Publication year Protocol Transparent Universal Plausibly Post-Quantum Secure Programming Paradigm Pinocchio[32] 2013 zk-SNARK No No No Procedural Geppetto[33] 2015 zk-SNARK No No No Procedural TinyRAM[34] 2013 zk-SNARK No No No Procedural Buffet[35] 2015 zk-SNARK No No No Procedural ZoKrates[36] 2018 zk-SNARK No No No Procedural xJsnark[37] 2018 zk-SNARK No No No Procedural vRAM[38] 2018 zk-SNARG No Yes No Assembly vnTinyRAM[39] 2014 zk-SNARK No Yes No Procedural MIRAGE[40] 2020 zk-SNARK No Yes No Arithmetic Circuits Sonic[41] 2019 zk-SNARK No Yes No Arithmetic Circuits Marlin[42] 2020 zk-SNARK No Yes No Arithmetic Circuits PLONK[43] 2019 zk-SNARK No Yes No Arithmetic Circuits SuperSonic[44] 2020 zk-SNARK Yes Yes No Arithmetic Circuits Bulletproofs[20] 2018 Bulletproofs Yes Yes No Arithmetic Circuits Hyrax[45] 2018 zk-SNARK Yes Yes No Arithmetic Circuits Halo[46] 2019 zk-SNARK Yes Yes No Arithmetic Circuits Virgo[47] 2020 zk-SNARK Yes Yes Yes Arithmetic Circuits Ligero[48] 2017 zk-SNARK Yes Yes Yes Arithmetic Circuits Aurora[49] 2019 zk-SNARK Yes Yes Yes Arithmetic Circuits zk-STARK[50] 2019 zk-STARK Yes Yes Yes Assembly Zilch[31] 2021 zk-STARK Yes Yes Yes Object-Oriented See also Arrow information paradox Cryptographic protocol Feige–Fiat–Shamir identification scheme Proof of knowledge Topics in cryptography Witness-indistinguishable proof Zero-knowledge password proof Non-interactive zero-knowledge proof References "What is a zero-knowledge proof and why is it useful?". 16 November 2017. 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Springer International Publishing. 11694: 701–732. doi:10.1007/978-3-030-26954-8_23. ISBN 978-3-030-26953-1. S2CID 199501907. Categories: Theory of cryptographyZero-knowledge protocols https://en.wikipedia.org/wiki/Zero-knowledge_proof https://en.wikipedia.org/wiki/List_of_knowledge_deities Category:Zero-knowledge protocols Category Talk Read Edit View history Tools Help From Wikipedia, the free encyclopedia The main article for this category is Zero-knowledge protocol. Pages in category "Zero-knowledge protocols" The following 6 pages are in this category, out of 6 total. This list may not reflect recent changes. A Anonymous veto network C Commitment scheme D Dining cryptographers problem F Feige–Fiat–Shamir identification scheme O Open vote network Z Zero-knowledge proof Categories: Asymmetric-key algorithmsCryptographic protocols https://en.wikipedia.org/wiki/Category:Zero-knowledge_protocols https://en.wikipedia.org/wiki/Law_of_Demeter https://en.wikipedia.org/wiki/Slack_(software) https://en.wikipedia.org/wiki/Uncommon_Knowledge https://en.wikipedia.org/wiki/Threshold_knowledge https://en.wikipedia.org/wiki/Timeline_of_knowledge_about_galaxies,_clusters_of_galaxies,_and_large-scale_structure https://en.wikipedia.org/wiki/Innatism https://en.wikipedia.org/wiki/Rationalism#The_innate_knowledge_thesis https://en.wikipedia.org/wiki/House_of_Knowledge https://en.wikipedia.org/wiki/Knowledge_Quarter https://en.wikipedia.org/wiki/Consilience_(book) https://en.wikipedia.org/wiki/Socrates#Virtue_and_knowledge https://en.wikipedia.org/wiki/Relativism https://en.wikipedia.org/wiki/Vidya_(philosophy) https://en.wikipedia.org/wiki/Knowledge_production_modes https://en.wikipedia.org/wiki/Local_knowledge_problem https://en.wikipedia.org/wiki/The_Postmodern_Condition https://en.wikipedia.org/wiki/Knowledge_translation https://en.wikipedia.org/wiki/Braiding_Sweetgrass https://en.wikipedia.org/wiki/Democratization_of_knowledge https://en.wikipedia.org/wiki/Knowledge_gap_hypothesis https://en.wikipedia.org/wiki/Certainty https://en.wikipedia.org/wiki/STOCK_Act https://en.wikipedia.org/wiki/Knowledge_Is_King https://en.wikipedia.org/wiki/Semantic_Scholar https://en.wikipedia.org/wiki/Knowledge_broker https://en.wikipedia.org/wiki/Route_knowledge https://en.wikipedia.org/wiki/Knowledge-based_processor https://en.wikipedia.org/wiki/Forbidden_knowledge https://en.wikipedia.org/wiki/Wikidata https://en.wikipedia.org/wiki/Encyclopedic_knowledge https://en.wikipedia.org/wiki/Knowledge_space https://en.wikipedia.org/wiki/Knowledge_level https://en.wikipedia.org/wiki/The_Sword_of_Knowledge https://en.wikipedia.org/wiki/Schema_(psychology) https://en.wikipedia.org/wiki/Pedagogy https://en.wikipedia.org/wiki/Experiential_knowledge https://en.wikipedia.org/wiki/Postmodernism https://en.wikipedia.org/wiki/Core_Knowledge https://en.wikipedia.org/wiki/Prop%C3%A6dia#Outline_of_Knowledge https://en.wikipedia.org/wiki/Karl_Popper https://en.wikipedia.org/wiki/Michel_Foucault https://en.wikipedia.org/wiki/Access_to_Knowledge_movement https://en.wikipedia.org/wiki/Hutter_Prize https://en.wikipedia.org/wiki/SECI_model_of_knowledge_dimensions https://en.wikipedia.org/wiki/Consilience_(book) https://en.wikipedia.org/wiki/Everyman_(15th-century_play) https://en.wikipedia.org/wiki/Abhij%C3%B1%C4%81 https://en.wikipedia.org/wiki/Ismail_al-Jazari https://en.wikipedia.org/wiki/Traditional_ecological_knowledge https://en.wikipedia.org/wiki/Pseudoscience https://en.wikipedia.org/wiki/Empiricism https://en.wikipedia.org/wiki/Scientist https://en.wikipedia.org/wiki/An_Essay_on_Criticism https://en.wikipedia.org/wiki/Ornithology#Early_knowledge_and_study https://en.wikipedia.org/wiki/Technological_pedagogical_content_knowledge https://en.wikipedia.org/wiki/Knowledge_Generation_Bureau https://en.wikipedia.org/wiki/University https://en.wikipedia.org/wiki/Knowledge_compilation https://en.wikipedia.org/wiki/Sherlock_Holmes#Knowledge_and_skills https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction https://en.wikipedia.org/wiki/Tree_of_Knowledge_(Australia) https://en.wikipedia.org/wiki/Vocabulary#Productive_and_receptive_knowledge https://en.wikipedia.org/wiki/Appropriation_of_knowledge https://en.wikipedia.org/wiki/Skepticism https://en.wikipedia.org/wiki/Bioprospecting https://en.wikipedia.org/wiki/Frame_(artificial_intelligence)#Frame_language https://en.wikipedia.org/wiki/Mathematical_knowledge_management https://en.wikipedia.org/wiki/Texas_Assessment_of_Knowledge_and_Skills https://en.wikipedia.org/wiki/Augustine_of_Hippo#Natural_knowledge_and_biblical_interpretation https://en.wikipedia.org/wiki/W._Edwards_Deming#The_Deming_System_of_Profound_Knowledge https://en.wikipedia.org/wiki/Follow-the-sun https://en.wikipedia.org/wiki/Non-interactive_zero-knowledge_proof https://en.wikipedia.org/wiki/Terry_Scott_Taylor#Knowledge_&_Innocence https://en.wikipedia.org/wiki/Omniscience https://en.wikipedia.org/wiki/Invention_of_Knowledge https://en.wikipedia.org/wiki/Theaetetus_(dialogue)#Protagoras%27_theory_of_knowledge https://en.wikipedia.org/wiki/Knowledge_neglect https://en.wikipedia.org/wiki/Scientia_sacra https://en.wikipedia.org/wiki/Knowledge_and_Decisions https://en.wikipedia.org/wiki/Proof_of_knowledge https://en.wikipedia.org/wiki/Factual_relativism https://en.wikipedia.org/wiki/Knowledge_Query_and_Manipulation_Language https://en.wikipedia.org/wiki/Knowledge-based_engineering https://en.wikipedia.org/wiki/Multi-factor_authentication https://en.wikipedia.org/wiki/Knowledge_survey https://en.wikipedia.org/wiki/Intellectual_capital https://en.wikipedia.org/wiki/Transcendentalism#Transcendental_knowledge https://en.wikipedia.org/wiki/Theory_of_knowledge_(disambiguation) https://en.wikipedia.org/wiki/A_Culture_of_Conspiracy https://en.wikipedia.org/wiki/A_Treatise_Concerning_the_Principles_of_Human_Knowledge https://en.wikipedia.org/wiki/Objectivity_(philosophy) https://en.wikipedia.org/wiki/Knowledge_regime https://en.wikipedia.org/wiki/The_Social_Construction_of_Reality https://en.wikipedia.org/wiki/Francis_Bacon#Organization_of_knowledge https://en.wikipedia.org/wiki/Knowledge-based_recommender_system https://en.wikipedia.org/wiki/Traditional_medicine#Knowledge_transmission_and_creation https://en.wikipedia.org/wiki/Information_silo https://en.wikipedia.org/wiki/World_Bank#Global_Operations_Knowledge_Management_Unit https://en.wikipedia.org/wiki/Philosophical_skepticism https://en.wikipedia.org/wiki/The_Knowledge:_How_to_Rebuild_Our_World_from_Scratch https://en.wikipedia.org/wiki/Bayes%27_theorem?wprov=srpw1_412 https://en.wikipedia.org/wiki/Mathematician https://en.wikipedia.org/wiki/Zoology https://en.wikipedia.org/wiki/Adam_and_Eve https://en.wikipedia.org/wiki/Foundations_of_the_Science_of_Knowledge https://en.wikipedia.org/wiki/Unity_of_science https://en.wikipedia.org/wiki/Nihilism https://en.wikipedia.org/wiki/Tabula_rasa Meaning of knowledge Linguistic According to the Oxford English Dictionary, the word knowledge refers to "Facts, information, and skills acquired through experience or education; the theoretical or practical understanding of a subject." "In this work on the concept of knowledge, Franz Rosenthal collected a number of definitions of 'ilm, organizing them according to what he saw as their essential elements (admitting that the list was ahistorical and did not necessarily conform to categories the medieval Muslim scholars themselves would have used). Among these definitions, we find the following: Knowledge is the process of knowing, and identical with the knower and the known. Knowledge is that through which one knows. Knowledge is that through which the essence is knowing. Knowledge is that through which the knower is knowing. Knowledge is that which necessitates for him in whom it subsists the name of knower. Knowledge is that which necessitates that he in whom it subsists is knowing. Knowledge is that which necessitates that he in whom it resides (mahall) is knowing. Knowledge stands for ( 'ibarah 'an) the object known ( 'al-ma lum). Knowledge is but the concepts known ( 'al-ma ani al-ma luma). Knowledge is the mentally existing object."[1] Islamic meaning Knowledge in the Western world means information about something, divine or corporeal, while In Islamic point of view 'ilm is an all-embracing term covering theory, action and education, it is not confined to the acquisition of knowledge only, but also embraces socio-political and moral aspects.it requires insight, commitment to the goals of Islam and for the believers to act upon their belief.[2] Also it is reported in hadith that "Knowledge is not extensive learning. Rather, it is a light that God casts in the heart of whomever He wills." [3] https://en.wikipedia.org/wiki/Ilm_(Arabic)#Meaning_of_knowledge https://en.wikipedia.org/wiki/Scientific_Knowledge_and_Its_Social_Problems https://en.wikipedia.org/wiki/Citation https://en.wikipedia.org/wiki/Problem_solving https://en.wikipedia.org/wiki/Modern_flat_Earth_beliefs https://en.wikipedia.org/wiki/Generosity#In_knowledge https://en.wikipedia.org/wiki/Amnesia https://en.wikipedia.org/wiki/Spherical_Earth https://en.wikipedia.org/wiki/Library_Genesis https://en.wikipedia.org/wiki/Third_eye https://en.wikipedia.org/wiki/International_Service_for_the_Acquisition_of_Agri-biotech_Applications#Global_Knowledge_Center_on_Crop_Biotechnology https://en.wikipedia.org/wiki/WolframAlpha https://en.wikipedia.org/wiki/Knowledge-based_authentication https://en.wikipedia.org/wiki/Pre-Socratic_philosophy#Knowledge https://en.wikipedia.org/wiki/Reinforcement_learning https://en.wikipedia.org/wiki/Magician_(fantasy) https://en.wikipedia.org/wiki/Physicist 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https://en.wikipedia.org/wiki/Lexicon https://en.wikipedia.org/wiki/Noble_Eightfold_Path https://en.wikipedia.org/wiki/If_a_tree_falls_in_a_forest#Knowledge_of_the_unobserved_world https://en.wikipedia.org/wiki/History_of_science https://en.wikipedia.org/wiki/Hematology https://en.wikipedia.org/wiki/Justification_(epistemology)#Justification_and_knowledge https://en.wikipedia.org/wiki/Discourse https://en.wikipedia.org/wiki/Unity_of_knowledge_and_action https://en.wikipedia.org/wiki/Tartary https://en.wikipedia.org/wiki/Philanthropedia https://en.wikipedia.org/wiki/Visualization_(graphics) https://en.wikipedia.org/wiki/Nightingale_Pledge https://en.wikipedia.org/wiki/Doctor_of_Science https://en.wikipedia.org/wiki/Expert_system https://en.wikipedia.org/wiki/Walker%27s_Hibernian_Magazine https://en.wikipedia.org/wiki/Critical_theory https://en.wikipedia.org/wiki/Scientific_management https://en.wikipedia.org/wiki/Autodidacticism https://en.wikipedia.org/wiki/Occult 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https://en.wikipedia.org/wiki/All_the_Knowledge_in_the_World https://en.wikipedia.org/wiki/Apocalypse_of_Adam https://en.wikipedia.org/wiki/Information_retrieval https://en.wikipedia.org/wiki/Scientism https://en.wikipedia.org/wiki/Human_settlement https://en.wikipedia.org/wiki/Akrasia https://en.wikipedia.org/wiki/Worldview https://en.wikipedia.org/wiki/Sophist https://en.wikipedia.org/wiki/Intellectual https://en.wikipedia.org/wiki/Knowledge_by_presence https://en.wikipedia.org/wiki/Science_and_technology_studies https://en.wikipedia.org/wiki/The_Open_Source_Definition#Open_Knowledge https://en.wikipedia.org/wiki/Philosophy_of_education https://en.wikipedia.org/wiki/System_administrator https://en.wikipedia.org/wiki/Logic_programming#Knowledge_representation https://en.wikipedia.org/wiki/Three_Sovereigns_and_Five_Emperors https://en.wikipedia.org/wiki/Old_wives%27_tale https://en.wikipedia.org/wiki/Children%27s_use_of_information#The_origins_of_knowledge https://en.wikipedia.org/wiki/An_Essay_Concerning_Human_Understanding https://en.wikipedia.org/wiki/Sheja_Dz%C3%B6 https://en.wikipedia.org/wiki/Second_modernity https://en.wikipedia.org/wiki/Phenomenology_(sociology) https://en.wikipedia.org/wiki/The_Open_Source_Definition https://en.wikipedia.org/wiki/Machine_translation https://en.wikipedia.org/wiki/Digital_library https://en.wikipedia.org/wiki/Economic_sector https://en.wikipedia.org/wiki/Encyclop%C3%A9die https://en.wikipedia.org/wiki/Cassell%27s_Book_of_Knowledge https://en.wikipedia.org/wiki/Persuasion#Persuasion_Knowledge_Model_%28PKM%29 https://en.wikipedia.org/wiki/Human_intelligence#Process%2C_personality%2C_intelligence_and_knowledge_theory_%28PPIK%29 https://en.wikipedia.org/wiki/Commonplace_book https://en.wikipedia.org/wiki/Episteme https://en.wikipedia.org/wiki/Scientific_theory https://en.wikipedia.org/wiki/Prolegomena_to_Any_Future_Metaphysics#Preamble_on_the_peculiarities_of_all_metaphysical_knowledge https://en.wikipedia.org/wiki/Lists_of_encyclopedias https://en.wikipedia.org/wiki/Certified_Ethical_Hacker https://en.wikipedia.org/wiki/Early_world_maps https://en.wikipedia.org/wiki/Lifelong_learning https://en.wikipedia.org/wiki/Theories_of_second-language_acquisition https://en.wikipedia.org/wiki/Advent_Online_Knowledge https://en.wikipedia.org/wiki/Word-sense_disambiguation#Dictionary-_and_knowledge-based_methods https://en.wikipedia.org/wiki/Women%27s_Ways_of_Knowing#Received_Knowledge%3A_Listening_to_the_voices_of_others https://en.wikipedia.org/wiki/Social_constructivism https://en.wikipedia.org/wiki/Universal_Decimal_Classification#0_Science_and_knowledge._Organization._Computer_science._Information._Documentation._Librarianship._Institution._Publications https://en.wikipedia.org/wiki/Statistical_potential https://en.wikipedia.org/wiki/Motor_learning https://en.wikipedia.org/wiki/Link_analysis https://en.wikipedia.org/wiki/List_of_polyglots 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